You still run into the problem with some phones not supporting different "generic" gaming sets. For example, iPhone doesn't support Java or Flash (Flash can be hacked in, Java can't as of yet). Android and Blackberry both do, though for Flash you will need to have a newer one.
Hmm.
You need to be more clear, still.
My phone uses J2ME and a 240x400 pixel capacitive touchscreen.
There are a ton of differences in those areas specifically, and without that information, it is nigh-impossible for us to be sure something will work for you.
Let's forget about iPhone, it's lack of compatibility with darn near everything makes it a bad example. For Android and Blackberry, or any phone with Flash, you can probably play some of the games on Newgrounds. I'm a little iffy on that though, my phone still runs 2.1 (will hopefully be upgraded to 2.2 in September) so it's not up to the flash 9 required to run most games. A lot of browser based games will play, if you're into that. With a halfway decent emulator available for pretty much any phone, you can play all the old GBA games for "free" (legally you should probably pay for them, I usually consider them abandonware since if I bought them it would be second hand anyways and the company wouldn't get the money). Android even has a PSX emulator (Blackberry and iPhone may as well, I only have access to the Android market), though it's tricky to set up and has some crashing and support issues.
When I get around to upgrading my phone, it'll be one that can run Dungeon Crawl
Dungeon Crawl: Stone Soup can't be run on any current phone that I know of. Not only is it a little too heavy (on my laptop it uses more memory than my phone has), it's written for the PC, with dependence on hardware that phones may or may not have. There are a few ones that run a full Linux OS that you might be able to get it to work on, but it's unlikely. Sorry. You might suggest that to them, and you might be able to get the Telnet version to work. There are other roguelikes on the popular phones though, I just got Nethack for Android.
It could probably be ported. Using Nethack's strategy of saving a lot of the things stored in memory to the hard drive (or flash card in this case), you could get the memory required down a single level. You would lose some of the complexity - no Jivya spawning slimes on your stash in Lair for example, but it would be functionally the same. Assuming you could get most of the behavior code ported, you would only need to modify it for a phone's diminished hardware specs and build a GUI designed for the more limited input methods of a phone. But you would need to talk to the Dungeon Crawl dev team about that (and be a pretty talented programmer) to pull it off.