Legendary NBC (and later CBS) play-by-play man Dick Enberg would often exclaim "Oh my!" The tone would vary based on the type of play. Nowadays, as the San Diego Padres' PBP man, he uses "Touch 'em all!" when a Padres player hits a home run.
The late Detroit Tigers announcer Ernie Harwell would often say when a batter took a called third strike, "...and he stood there like the house by the side of the road and watched that one go by."
"...and that ball is fouled into the stands and caught by a fan from (insert name of nearby city/town/suburb)."
"Hello, Canada, and hockey fans in the United States and Newfoundland, and an extra big hello to Canadian servicemen overseas." From Hewitt's radio opening in the Forties, prior to Newfoundland joining Canada in 1949. Has been replayed on HNIC over the years, and occasionally at least "Hello, Canada", if not more, has been incorporated into the show open.
Other broadcasters have used "He shoots, he scores" or a slight variation thereof, such as Detroit's Bruce Martyn and his successor Ken Kal (usually going falsetto on "scores"), or Pittsburgh's Mike Lange ("Heeeeeeeeeeeeeee shoots and scores!").
Harry Caray, the Cubs' announcer: "There's a drive! Waaaay back! It might be ... it could be ... it is! A home run! Holy cow!"
Also used "Cubs win! Cubs win!" after the final out (assuming they did in fact win, of course).
Ian Darke has "CAN YOU BELIEVE THIS?" after a particularly amazing goal. See Landon Donovan and Abby Wambach at the 2010 Men's and 2011 Women's World Cup, respectively.
Toronto Maple Leafs announcer Joe Bowen is known just for: "Holy mackinaw!"
John Sterling's famous "Yankees win! Theeeeeeeeeeeeee Yankees win!"
Legendary play-by-play man Keith Jackson has had "Whoa Nelly!" tagged as his catchphrase - despite his own estimation that he's only said it three or four times in his four-decade career.
The White Sox' Ken "Hawk" Harrelson not only has one of the most awesome home run calls in the business (several variations on "Stretch! That ball hit way back! He looks up... you can put it on the booooard... YES! YES!"), he also has one for when a White sox pitcher strikes out an opposing batter: "He gone!" He also has "And this ball game is OVAH!" for when the Sox win, "Mercy!" for a particularly crazy play and "It's all good!" for a great play by a Sox player. Hawk could probably call an entire game using nothing but his catchphrases.
How the heck did we get this far without Michael Buffer's "Let's get ready to RUMBLE!"
Which he alters for the finals of the World Series of Poker, where he traditionally kicks off the final table with "Let's get ready to SHUFFLE UP AND DEAL!"—the latter part alone being the usual starting phrase.
Pittsburgh Penguins radio play-by-play announcer Mike Lange is thought to have coined the phrase "Elvis has left the building!" Other catchphrases include:
"Scratch my back with a hacksaw!"
"Buy Sam a drink and his dog one, too!"
"Get in the fast lane, grandma: The bingo game's ready to roll!"
"Beat him like a rented mule!"
"He doesn't know whether to cry or to wind his watch!"
Olympic swimmer Ryan Lochte has 'Jeah!', a phrase which he has described as basically meaning 'good' and reached memetic levels during the London Olympics. Speedo has produced this useful video to show all the different meanings of 'Jeah!'.
Sam Rosen's "It's a Power Play goal!" whenever a New York Ranger achieves as much.
During Dan Patrick and Keith Olbermann's SportsCenter tenure; both would borrow the phrase (in Olbermann's case; it doubled as a Shout-Out since Rosen was Olbermann's first boss when Keith started out at UPI Radio).
Los Angeles Dodgers announcer Vin Scully always opens his broadcasts with, "Hi, everybody, and a very pleasant good afternoon/evening to you, wherever you may be."
Spurred on by Chris "He COULD! GO! ALL! THE! WAY!" Berman, Dan "En Fuego" Patrick, and Keith "He pulled a groin. His own, we hope" Olbermann, catchphrases seem to be a requirement to be a SportsCenter anchor - particularly the flagship 11PM EST broadcast.
Berman spoofed himself with his appearance in Hootie & the Blowfish's music video for "Only Wanna Be With You", where he shouts despairingly "They do not! Go! All! The! Way!"
Dave Niehaus, "My, oh my!"; and "Swung on and belted...!"
It seems that most sportscasters have a catchphrase assigned to them by their network or the team that they broadcast for along with the keys to the broadcast booth. Of course, baseball announcers are noted (notorious?) for specific catchphrases they use when a player hits a home run (known in the jargon as "home run calls"). Entire books could be (and probably have been) written about noted broadcasters' home run calls. Subverted/spoofed in a Bud Light commercial when it's suggested to Bud Light pitchman (and broadcaster) Joe Buck that he needs a home run call. The one they come up with? "Slam-a-lam-a-ding-dong."
As long as we're on ESPN sportscasters, we have to mention Stuart Scott, and his prolific use of "Booyah!"
Horse racing: "..And they're off!" (or "off and running")
"And down the stretch they come!"
"It's a beautiful day for football!", for every announcer (and the whole crowd) at Michigan State University's Spartan Stadium. They say this at every game—irrespective of whether it's a bright, clear, crisp fall day or a humid late-August steamer or a thunderstorm or even snowing. Yes.
And of course the universal race starter "Gentlemen, start your engines!" (changed to "Drivers" when there are women in the field)