Pro Football Hall of fame Running Back Jim Brown is a great example of this trope. Brown was stronger than many linemen, faster than a lot of defensive backs and he never missed a game. The result was leading the league in rushing yards 8 times in 9 years.
In the NBA the center is usually the biggest guy on the team, with an average height of 7 feet. While the NBA has known fast centers in the past, Mr. David Robinson puts them all to shame.
The Big Dipper Wilt Chamberlain would have to as well. He could run the hundred meters in 10.9 seconds and probably could have been an Olympic Hurdler. He also is in contention for being one of the strongest men in the history of the association with anecdotes of him dunking with smaller players actually just grabbing onto his arms and being taken for a ride.
Due to the increasingly fast-paced nature of NBA basketball, the best Big men (Power Forwards and Centers) in today's NBA have to be Lightning Bruisers: strong enough to box out opposing centers yet fast and athletic enough to be a factor on motion offenses. Current NBA players who fit this archetype well include Anthony Davis, LaMarcus Aldridge, Blake Griffin, Chris Bosh, Draymond Green, and Al Horford.
Draymond Green is a weird example: While he is relatively small (6'7") for a starting Power Forward, he is strong enough to tussle with larger bigs in the paint (a-la Charles Barkley), allowing him to defend and score efficiently near the basket. Likewise, he is fast enough to be able to slash effectively and occasionally score from midrange. These factors have made him a perfect piece for the NBA Champion Golden State Warriors, whose system revolved around motion offenses, fast break plays, and a strong defense. Green's strengths have even allowed him to play CENTER in some small-ball packages, despite being shorter than, say, Anthony Davis or Marc Gasol.
The "unicorns" of the NBA are insanely fast, athletic and coordinated 7-footers who have led some to believe that the league is trending back towards an era of dominant big men. Most are in their early twenties at the moment: Giannis Antetokounmpo, Karl-Anthony Towns, Kristaps Porzingis, Joel Embiid, and even the aforementioned Anthony Davis. The man who coined the term himself, Kevin Durant, is also an example of this trope.
Basketball player Charles Barkley was almost unstoppable under the basket, putting up unheard-of rebound and field-goal percentage numbers for a player his height (listed at six-foot-six but in reality under six-foot-five). He was also incredibly quick, and could get a defensive rebound or steal, dribble the length of the court, and finish with a dunk without any opponent being both fast and strong enough to do anything about it.
Most people remember Muhammad Ali for his lightning fast speed, but he was also 6'4, 220 pounds, had an iron chin, an incredibly durable body and heartfor days.
Modern Defensive Ends and Outside Linebackers in American Football. Mentioning the names Von Miller, JJ Watt, Khalil Mack, Cameron Wake, Ezekiel Ansah, Jason Pierre-Paul and Justin Houston will strike fear into the hearts of many a Quarterback (and Offensive Tackle).
Special mention, however, must go to the late, great Reggie White. 6' 5", 300 pounds, could run a 4.6-second 40 yard dash, and in his prime was stronger than any offensive lineman he was matched up with. In fact, one of his favorite methods of sacking a quarterback was simply pushing the guard backwards until he reached the QB.
By the same token, many inside linebackers in American football are also lightning bruisers, being both agile and fast as well as hard-hitting and punishing when making a tackle or sack. Guys like Luke Kuechly, Bobby Wagner, Sean Lee, and Jamie Collins are some of the most diverse defensive players in NFL history, being able to get sacks, forced fumbles, and interceptions.
Also of particular note are Safeties: While they're smaller than Linemen or Linebackers, they also have to be tough hitters and strong tacklers, since they're the "Last Line Of Defense" against opposing receivers and rushers. Additionally, the threat of pass plays forces most safeties to take up a coverage role, thus requiring them to be fast enough to cover wide receivers (and, occasionally, running backs and tight ends). Notable safeties of the past who fit the "Move fast and hit hard" archetype of the Lightning Bruiser include Ronnie Lott, Brian Dawkins, the late Sean Taylor, Steve Atwater, Ryan Clark, Ed Reed, and Troy Polamalu. Active safeties who fill this role well include Kam Chancellor, Landon Collins, Earl Thomas, Eric Reid, and Eric Berry.
On the offensive side of the ball, you have some "power-running" power backs who are fast enough to bamboozle opposing defenders and strong enough to stiff-arm tacklers and shed blockers, essentially making them the Power Forwards of American football. Some good examples include Marshawn Lynch, Adrian Peterson, and Le'Veon Bell.
Tight Ends have been evolving this way since Kellen Winslow, to the point that the best Tight Ends active in the NFL are basically uncoverable one-on-one. Players like Jimmy Graham, Rob Gronkowski, and Jordan Reed are too fast for Linebackers and too big and strong for Cornerbacks, and you can count the number of Safeties who can match them in both categories on one hand.
Having shades of this is a requirement for playing at a competition level - the WFTDA minimum skills require the skater to have the ability to both absorb and deal out a hit and remain standing, jump over a six-inch obstacle, skate a complete lap in 13 seconds from a standing start and 27 laps in 5 minutes.
Given the division into weight categories, most fighters are either too small to have real destructive power, or, on the other end of the spectrum, the heavyweights can end careers with a single punch but lack the speed/gas tank to keep it up. In the middleweight (185lbs) and light heavyweight divisions (205lbs), however, there are:
Deceptively fast powerhouses, such as middleweight Yoel Romero, the Olympic wrestler who knocked out Chris Weidman with a flying knee, and
Overwhelmingly strong nimble guys, such as Jon Jones and Alexander Gustafsson in the light heavyweight division.
There's also Brock Lesnar, also covered on the Professional Wrestling subpage, a heavyweight who is monstrously strong, dangerously fast, and difficult to knock out.
Junior Dos Santos, Andrei Arlovski, Mirko Cro Cop and Alistair Overeem. All of them are heavyweights who strike faster than a lot of lighter guys.
Fedor Emelianenko, in his prime, is the prototype for lightning bruisers in MMA. He mostly made his name by being the only heavyweight in his era that could move with the speed of a lightweight, which, combined with his striking power and precision, and his masterful ground game, earned him the nickname "The Last Emperor". He could take punishment as well: Kevin Randleman suplexed him hard enough that both fighters went airborne, sending Fedor crashing down on his head. Fedor won the fight 48 seconds later.
UFC Featherweight champ Jose Aldo fights at 145 lbs and is known for his amazing knockout power in his hands, feet and knees.
UFC Middleweight champ Anderson Silva is a tall, skinny fighter at 185 lbs and is known for his one-punch knockout power as well as his effortless evasion on the feet.
Mario Williams, the defensive end for the Buffalo Bills. He's 6 foot 7, close to 300 pounds, and he runs the 40 yard dash in under 5 seconds. (4.65, to be exact). Or Albert Haynesworth. 6'6", 350 pounds, runs the 40 in 4.93... before he got fat and lazy.
A lot of the good heavy-weights in "Amateur" Wrestling (e.g. College, High School, and Olympic) tend to be like this. They're big, beefy, but they can go about as quickly as a 105 pounder if they've trained right.
A lot of sumo wrestlers fall into this category. Not all of that body mass is fat.
Mike Tyson was not a large heavyweight, but he punched extremely fast and extremely hard, dispatching many of his opponents with almost insulting ease.
As a matter of fact, every single professional boxer may count. Some boxers focus on punch power, punching speed, evasion or blow taking, but there's no such a thing as a slow, weak or fragile boxer.
Many power forwards in the sport of hockey are this. I don't think anyone ever accused Cam Neely or Jarome Iginla of being slow. Most players 6'3 and over are somewhat slower than others but there have been (and are) multiple exceptions to this.
Even a slow hockey player is a fast athlete overall. Training regimens for track athletes and hockey players overlap quite a bit.
The general positions of the two flankers and the Number 8 (also known as the 'back row' of the scrum) need to be Lightning Bruisers. Faster than the front row, and bigger than the backs, they need to be powerful enough to lend their strength to the rucks, scrums, and mauls, as well as fast enough to break off, enter the ball-carrying phases, and make tackles. Good examples of Lightning Bruisers in these positions are All-Black openside flanker Richie Mc Caw and Springbok flanker Schalk Burger.
The modern game has evolved to such an extent - and was so hard-hitting in the first place - that most rugby players need to be Lightning Bruisers. Props, traditionally the big slow heavy ones, need to be fast enough to get to the breakdown, while the traditionally zippy wingers now need to be strong enough to power through potential challenges.
All Black winger Jonah Lomu. Powered through those in his path, and outran everyone else.
English center Manu Tuilagi is famed for his strength, despite being a center.
The most well known example in Australian Football is Barry Hall. Built like a brick shit house and incredibly strong but faster than any tall defender.
Lebron James. 6'8", about 270 pounds (most guys his height in the NBA are about 30-50 pounds lighter), also one of the quickest, most agile players in the NBA. It was said of him that while Magic Johnson was the first "point forward", James was the first "point linebacker". Apparently he was an absolute monster as a high school wide receiver.
He was first-team all-state as a sophomore. (He came into the league at 6'8" and wasn't much smaller then than he is now.) Many people speculate to this day on What Could Have Been if Lebron had picked football over basketball.
Two of the best handballers in the world, Nikola Karabatic (France) and Mikkel Hansen (Denmark), both fall well under this category. Both stand at 1.96m and weigh over 100kg. While not having the pace of a winger, they're both fast and technically strong. They also have great view of the game and extremely powerful shots. Both started out as left backs, and they're both becoming playmakers (Karabatic primarily is, while Hansen is sometimes used on the position).
Manny "Pac-Man" Pacquiao. The man started his career at 106 pounds, has advanced all the way to 147 (almost unheard of in Boxing). And his KO percentage has risen, while he retains the same blinding handspeed he had at lower weights. Ricky Hatton got a little taste of that combination earlier this year, as did Miguel Cotto, both men billed as "bigger and stronger" than Pacquiao, until he put a thoroughly one-sided beat down on both of them. Hatton got knocked out in the second round, and the ref jumped in to save Cotto in the final round of their fight.
Roy Jones, Jr. Possibly the fastest pound for pound fighter in boxing history, Roy Jones also had incredible knockout power for the early part of his career. Watching Roy Jones is an experience in and of itself, he sits back and strikes like a viper. He's like a ninja in the ring...just watch his first knockdown of journeyman Richard Hall. I'm pretty sure he teleports at least once.
Sugar Ray Robinson is still considered the greatest boxer of all time by boxing experts. Thanks in part to his blink-or-you'll-miss hand speed and ungodly punching power, he destroyed his opponents with his unequaled talent and the sheer ferocity of his attack. Ringside attendants said it was like watching a dancer with the killer instincts of a tiger.
Mark Recchi is small for a hockey player who plays a physical style (5'10, 180 pounds) but early in his career was nicknamed "The Wrecking Ball" for his propensity to crash into opponents, many larger than himself. Pat Verbeek, also qualifies, earning the amazing nickname "The Little Ball of Hate". Unlike Recchi, he was also known for fighting.
Rafael Nadal, one of the greatest current and all-time tennis players, is incredibly fast, strong and has plenty of endurance. This is one of the reasons why he was able to challenge Roger Federer's skills. His one main drawback is that he tends to be injury-prone; of the Big Four, he is the only one who regularly taps out of Grand Slams, and tennis commentators speculate that his career might be cut short because of it.
Novak Djokovic, in the past, was skillful and fast enough to challenge Federer and Nadal. But he was mostly overshadowed by them partially due to his body not having enough stamina. Come 2011 and Djokovic overshadowedeverybody, very mostly thanks to him becoming more skillful, stronger, faster and tougher. His increased endurance rivaled even that of Nadal's. Djokovic even managed to beat Nadal in the 2012 Australian Open final which lasted 5 hours and 53 minutes (which is the record for longest final for any Grand Slam).
In Soccer/Football/Calcio, Box-to-box midfielders are meant to be this, with their combination of attacking power, defensive prowess, physical strength, stamina, and pace. Current examples include Arturo Vidal, Paul Pogba, Luka Modric, Aaron Ramsey, and Yaya Toure. Past examples include Paul Scholes, Steven Gerrard, Deco, and Roy Keane.