This app was mentioned in 3 comments, with an average of 1.33 upvotes
For basic use try MAME4droid (0.37b5)
https://play.google.com/store/apps/details?id=com.seleuco.mame4all&hl=en
Most of the negative reviews come from people that don't understand how it setups its directory paths, just let it do its own. Also from not using the correct romset most likely(?)
MAME can be a bit of a mess in terms of ROM compatibility. There's a separate version available that may support other games as well.
Final Burn Alpha (aFBA) is also a good choice for arcade titles, and I've found it simpler for some than either version of MAME (for Street Fighter 3: 3rd Strike, for example).
As for the games, You've listed two of my biggest suggestions with X-Men and Simpsons. Most of what I know is fighters and beat-em-ups.
That's all I can think of off the top of my head.
Also if you are into classic games there's always a reason to check out MAME. I love MAME especially when i got friends over and you want to roll a nice Double Dragon or Final Fight session.