The Adventures of Batman & Robin
This was the first DC game I ever played. I had this for the Sega Genesis, and apparently is different on the Sega than it is the SNES, so this is for the Sega version.
The game is based on Batman the Animated Series and has matching art styles. It is a side-scrolling "shooter". You run from the left of the screen to the right shooting batarangs at enemies. If they get close, you punch them, but it's mainly a "run and gun".
Honestly, it isn't a perfect game, but I would play anything related to the animated series. It is very difficult though, I just recently got passed the first level, and I've been trying for years!
Hahaha, no. Just kidding.
Justice League Heroes
I played the PSP version, so I can't speak about the console version, but the portable version was great. In each level, you battle a number of villains and henchmen, all Justice League themed of course. You are partnered up with another Justice Leaguer and can switch between then at any time. You have seven characters to chose from in the beginning:
As the game progresses, you unlock more characters: Aquaman, Green Arrow, a few more Green Lanterns, etc.
Lego Batman: The Video Game
I almost hate to say it, but this might be my favorite DC based game. This game plays like most other Lego games, you start a stage, then run from one place to another killing bad guys and collecting "Lego parts".
As with all other Lego games but Lord of the Rings, the story is told without any dialogue, which I find extremely neat. In the game, pretty much everyone escapes Arkham, and the villains split off into groups. Riddler, Penguin, and the Joker all lead their own group populated by nameless henchmen and plenty of well and lesser known villains.
This game has tons of unlockables and amazing replayability. Co-op is definitely the way to go, but the game isn't bad by yourself at all.
Mortal Kombat VS DC Universe
The title here kind of explains the game, it's basically Mortal Kombat with DC characters thrown into the mix. At first, I wasn't sure what to think. I couldn't possibly see these characters work well together in a blended universe, but I think it turned out great.
The game features your basic Mortal Kombat line-up along with many members of the Justice League plus Catwoman (who is kind of a Justice Leaguer now), the Joker, Lex Luthor, and a few others.
The story mode did a nice job of trying to get these universes together. You get two options, to see the story from the Mortal Kombat perspective or the DC perspective. Both are worth playing. My only real complaint about this game is lack of unlockables. There are two unlockable characters, but I always love finding new characters to add to the roster throughout the game.
Batman: Arkham Asylum
Alright, so any Batman should have played this by now, but I keep finding people who haven't. If you haven't, stop reading and start playing. There is nothing else for you here.
Arkham Asylum is a third-person adventure style game. It focuses on combat and straight adventure gameplay. It is a perfect combination. The combat is extremely addictive and much easier than it looks. The puzzles are not necessarily challenging, but make you think a bit.
The story is about Batman bringing Joker to the asylum and he essentially takes it over. So, Batman is in Arkham with most of his dangerous super-villains out on the loose. Batman faces Scarecrow, Killer Croc, Zsasz, Bane, Poison Ivy, and other iconic villains.
Also, some consider this a continuation of the animated series, as some of the designs are similar and the voice actors for Batman and the Joker, among others, return from the animated series.
This game really is a near perfect game, or at least seems near perfect until you play...
Batman: Arkham City
This game is a sequel to Batman: Arkham Asylum. I've had multiple friends play this, but not Asylum. Do yourself a favor and play both.
The story takes place a little while after the first game, I won't ruin the story of the first game, but essentially Arkham Asylum is no longer usable. Blackgate Prison is also burnt down prior to the events of Asylum, so now there is literally no place for all these Gotham villains. Dr. Huge Strange creates Arkham City, a portion of Gotham walled off and filled with bad guys. Think Escape from New York. At first, I thought this premise was stupid, but after playing it, I love it.
The game plays very much like the first one, but has a bit more "open world" to it. You are free to go where you wish as long as you are inside of Arkham City. In the story, Bruce Wayne is thrown in as a political prisoner. Bruce calls for his suit to drop, and after a very cool opening battle, we get the play as Batman again.
This game adds numerous villains, Mr. Freeze, Catwoman (ally I guess), Talia, Ras, Dr. Strange, the Mad Hatter, among many others. There are tons of Easter eggs throughout this game, any Batman fan will love it just for that.
Movie Based Games
While not perfect, this game based on the movie was the best way as a kid to play out this movie. The game is basically a side-scrolling "beat 'em up". It's the basic setup we are used to, fight from left to right, battle a boss at the end. It doesn't stand the test of time, but was great when I was eight.
Batman Begins: The Video Game
Before I say anything else, don't expect this to be an Arkham like game in the Nolan-verse, it plays more like a Splinter Cell game with Sam Fischer is a Batman suit.
Batman Begins is a stealth-based combat game based on the film of the same name. The story is more or less the same, it just expands a little bit. The game focuses of scaring enemies and sneaking up behind them. If stealth games aren't your thing, stay clear. If you are a Metal Gear or Splinter Cell fan, I would recommend giving this a try. It still doesn't look too bad for being a generation old.
This is technically DC so I'm putting it on here. This game is based on the movie and is pretty much just a "beat 'em up". I honestly love this game, but if it wasn't Watchmen themed it wouldn't have much going for it.
In the game, you can play as Rorshach or Nite Owl II. The game kind of relies of team work, but if you are playing single player, the AI does a good enough job. You more or less run around in the 1970s busting up gangs. In the film, Nite Owl II mentions him and Rorshach teaming up to stop the gang problem, I can only assume this is what he is talking about. I recommend this to any Watchmen fan, even if you don't like the movie.
DC Injustice: Gods Among Us
I have talked about this game here so much, it probably seems like I'm getting paid to talk about.
Injustice is a new fighting game from the creators of Mortal Kombat. There is a demo available, and the game seems promising. It plays just like Mortal Kombat, but will be straight DC characters. I've read the tie-in comic, but I'll try not to give much away. Essentially, the Joker gets some fear toxin and convinces Superman that Lois Lane is Doomsday. Bad things happen after that! This game drops tomorrow!