There are five game modes in
Dragonball Z: Budokai: Story, World Tournament, Duel, Practice and Edit Skills. Unlike a lot of other fighters, each of these modes affects the others. Winning battles in one mode will allow you to use characters in others. It will also allow you to collect money to be used at Mr. Popo's shop in order to gain skills that will in turn allow you to customize characters to be used in battles and thus earn more skills and money.
Story Mode takes you from the beginning of Dragonball Z (when Goku introduces his son Gohan to the rest of the gang) to the end of the Cell Games (and Goku's decision to stay in Otherworld). Unfortunately, the actual story given in this mode is rather quick and gives absolutely no details about the events that happen. Most of it is given as if it is review --apparently the game assumes that the player is already familiar with the storyline. Now I am not saying that the game should give the kind of detail seen in the Dragonball Z: Legend of Goku line, but there were some story elements that shouldn't have been overlooked and were.
But this mode does give you a chance to do more than just fight (well occasionally). For example - when you defeat Raditz as Goku, you put Goku's brother in a full nelson and you have to keep the evil Saiyan in the center of the screen while Piccolo attempts to shoot his Special Beam Cannon at Raditz.
It is the Story mode where you unlock most of the characters and a good bit of the skills. Each time you defeat an enemy, you gain the ability to use them in the Practice, World Tournament and Duel Modes -- as well as adding to their skills with the Edit Skills mode. This is how you get Nappa, Captain Ginyu (after you defeat him as Goku), Android 18 and a few others.
World Tournament Mode is set up just like the tournament in the show -- you lose when you are KOed or Ringed Out (actually most of the times that I lost were by being Ringed Out). It starts with eight characters and one by one the characters fall. If you make it to the final round, then you are guaranteed money, but you get more depending on your ranking (runner up or champion) and the level of the tournament (Novice, Adept and Advanced). This money is used to pay for skills in the Edit Skills Mode.
Duel Mode pits you against either another player or the computer (or puts the computer against itself if you so wish it) and allows you to test your skills outside of the World Tournament and Story modes.
Practice Mode is similar to Duel. It is you against an opponent of your choosing and it gives you a chance to try out different combos and attacks in order to see what deals the most damage. The numbers given during the 'battle' show you various stats including most hits and most damage.
Another interesting feature in the fighting modes in this game is that occasionally the two combatants enter into the 'Burst Zone' where you have to rotate the analogue stick constantly while rapidly pressing the punch and kick buttons -- no damage is actually dealt in this sped up mode, but at the end, one person will deal out a powerful blow to the other and take a lot out of the loser's health bar. As far as which one will win - I haven't figured that part out yet.
What I feel to be the most intriguing part of Budokai is the Edit Skills Mode. In this mode, you can buy skills to be used with the unlocked characters. On top of that, you can actually trade these skills (because they come in the form of Capsules) with other players. This feature adds an RPG element to the game.