Broken Base: When it comes to a lack of Budokai 2 in the HD collection, do you not mind? (between the superior single player content of the first game, and the superior gameplay of the third, seeing Budokai 2 is an unnecessary Master of None), or does the collection feel incomplete without it?
Character Tiers: Not as bad as some other fighters but they're definitely present. Omega Shenron is top tier due to powerful combos and by default having 7 base ki bars, meaning he fills up to max ki without having to charge, and Piccolo, Cell, and Dabura are up there with him because of their fast ranged physical combos. Bottom tier is Saibaman and Mr. Satan.
In Infinite World, Yamcha is the highest tier character in the game. Why? Because his basic punch has more priority than anything else in the game. As long as you just keep spamming his normal punch and cancelling into it (via a frame-lock abuse) so the combo doesn't end, the enemy can never even fight back.
Contested Sequel: Infinite World is this to Budokai 3. Reasons for this include it actually removing characters and features and not adding any new stages, which makes it feel more like an expansion pack than an actual sequel.
Crowning Music of Awesome: The game's soundtrack is commonly considered to be very well done, especially the opening themes from 2 onward.
Enjoy the Story, Skip the Game: The gameplay of the first Budokai is really shallow, and repetitive, compared to it's sequels. That said, it's story mode is an admirable, cinematic attempt at retelling everything from the Saiyan Saga to the Cell Saga, while being Truer to the Text than the first anime adaptation, and was basically Mortal Kombat 9 long before the latter was a thing.
Fridge Brilliance: Notice how in Infinite World, GT Goku's Super Kamehameha is the same one he blew Commander Black to bits with in the movie The Path to Power., which is based on the original Dragon Ball. Why's this? Because technically the Goku in that movie was GT Goku thanks to using the same colour scheme as GT's depiction and his art style (facial structure and such) more resembling GT than the original Dragon Ball!
Game-Breaker: Piccolo's Light Grenade in Budokai 2 & 3. It only costs half a ki bar AND does some pretty heavy damage. In the first Budokai the damage it does isn't as much though, and you can't spam it like you can in 2 & 3.
Narm: The PAL version of the first game uses the Japanese voices whilst having an alternate translation for Story Mode...which features weirdness like Vegeta calling people "Aunt Sallies" and Bulma expressing sadness at how Goku "was able to escape from Namek" (seriously) while the cutscene showed him...kinda failing, (He escaped but besides that...) and at one point translates Cell's angry growl of "Chikushou!!" ("DAMMIT!") as "Shucks!!" On the other hand it does subtitle one of Android 18's lines as "Oh, Crap!..." and has a few instances of "Damn" here and there.
No Problem with Licensed Games: Each game in the series is generally a competent fighting game in its own right, benefiting greatly from familiarity with the characters from the show and manga. The third game with a massive cast, beautiful cell shaded graphics, long story mode that is faithful to the series (covering then entirety of DBZ, along with some surprise stories and guest fighters from both the prequel Dragonball and the sequel series Dragonball GT), solid gameplay mechanics and epic ultimates that capture the essence of the show perfectly, is considered the best of them all.
Pandering to the Base: Not just the cast of characters (which includes guys like Broly in 3) but what attacks they have, such as Tien having his Dodonpa and Volley Ball Fist, which he never uses in the Z series, not to mention costumes. Its quite fun being able to transform Vegeta into his Super Saiyan 2 or Majin form in his old Saiyan Saga armour.
Scrappy Mechanic: The Luck-Based Mission that is 3's Dragon Rush, in which you have to press a button and hope that your opponent fails to press the same button. You've got a very slim chance that you'll press a different button from them every single time. For weaker opponents, this isn't so bad, but it could easily cause you to lose the fight against stronger opponents like Cell and Kid Buu.
For Budokai 3, Hyper Mode was pretty much very unsafe and drained all your ki in one shot if you couldn't properly use it to land big damage or perform your ultimate. That, and Dragon Rushes were both abused heavily by the AI as well. Some people were glad that they were removed in Infinite World.
Surprisingly Improved Sequel: Budokai 3 is considered a vast improvement on the previous games. It added in the ability to fly up or down while dashing, teleport and dodge counters, more individualized physical combos for every character, greater variety in the special moves (most characters have a beam special and a physical combo special with varying properties), as well as the Dragon Rush mechanic and a new quick time event for Ultimate moves. Said special moves and ultimates alike also gained much more simplistic inputs. Oh, and it also added beam struggles, an icon of Dragon Ball Z that had somehow been absent in the first two games.
Suspiciously Similar Song: Many of Kenji Yamamoto's works sound eerily similar to songs by Finnish power metal band Stratovarius. The most obvious is the series Warrior from an Unknown Land compared to Stratovarius' Infinity. note Doesn't make Budokai's soundtrack any less awesome, though. In fact, years after the Budokai games were released, Yamamoto was fired because Toei found out about his plagiarism. The HD collection of the Budokai games uses a completely different soundtracknote ...or, to be more accurate, a mish-mash of the soundtracks from Budokai Tenkaichi 2 and 3, Raging Blast, Tenkaichi Tag Team and Ultimate Tenkaichi.
That One Boss: When playing as Goku, Budokai 3 has Cell. Before him, none of the previous bosses really stand too much of a chance (with the possible exception of Frieza in his full power form). Cell has more health than you, and is incredibly durable to most of the attacks that you have unlocked at this point. The Kamehameha sort of helps, but good luck landing a hit on him with it because he usually blocks it or moves out of its way.
The battle against Super Buu in Tien's story in 3 is also really tough, employing Perfect-Play A.I. with a stronger and more-versatile moveset than poor Tien.
Budokai 1's Legend of Hercule mode (in which you fight all of the Cell Game competitors as Hercule) has the fight against the Cell Juniors. During the battle you're hit with a major case of Hitbox Dissonance, as half of your attacks will fly right over the Cell Juniors' heads. Doesn't help that you have to beat them as, well, Hercule.
The Kid Buu fought at the end of Budokai 2's Dragon World haunted many player's nightmares.
Android 19 in Budokai's story mode. He's already one of the strongest characters, and you have to fight him with the heart virus chewing through your lifebar. Even more irritating because it's a Heads I Win, Tails You Lose fight. If nothing else, it does accurately recreate Goku's experience in the series of being beaten half to death mid-heart attack.
Visual Effects of Awesome: Most of the ultimates look fairly impressive in the first game, and then its cranked up big time from 2 onward, especially when you use certain world-destroying ultimates that change the arena into one of the two "ruined" stages. Using a sphere-shaped or explosion-based super move gets one of two scenes of the ball exploding on the planet's surface giving the player an epic view from the planet's orbit. Using a beam type ultimate, you see the beam shooting outward from the planet, also viewed from orbit. And the beam is gigantic if said successful ultimate was Super Saiyan 4 Gogeta's 100x Big Bang Kamehameha.
What The Hell, Casting Agency?: In Budokai 1, one wonders why Great Saiyaman, a Buu Saga character mind you, made it into a game that only went up to the Cell Saga, aside from popularity.
What the Hell, Hero?: In Burst Limit there's a partner ability called "Risking it all for a friend" (which is a recreation of what Piccolo did for Gohan in the fight with the saiyans). If you have Goku partnered with Raditz and this is activated, Goku's reaction to his brother sacrificing his own life for him comes across as downright cruel:
[Raditz throws himself in front of the blast about to hit Goku]
Raditz:[In pain] Kakarot...don't die...
[Raditz collapses and the game cuts back to the fight]