Doom Touch is very well done port of prBoom+ to Android:

https://play.google.com/store/apps/details?id=com.beloko.doo...

It's capable of playing the original trilogy as well as many classic levels and level-sets that are marked as doom2.exe, limit-removing, and BOOM compatible.

You can get DOOM for iOS. Plays particularly well on an iPad.

I forgot to mention that I hate touch controls. Something more like PSP/Nintendo DS/gcw-zero/bluetooth controller is more likely...

Same here. One thing I can recommend is to avoid 'Doom RPG' from iD. It's turn based, and has none of Doom's character.