There are alot of such games so a list would be good, both official and unofficial ports (unofficial might require to have the original files to copy to a folder). As well there are some improvements Sonic the Hedgehog (possible to play with tails and knuckles, wtf) iOS/Android Sonic the Hedgehog 2 iOS/Android Sonic the Hedgehog 3 iOS/Android Sonic CD (With tails like above, option to switch between the Japanese Soundtrack and creepy American Soundtrack) iOS/Android Jazz Jackrabbit (Actually port of OpenJazz for android, needs original files. If you want you can get the shareware demo on it. ALSO ALMOST IMPOSSIBLE DUE CONTROLLS) Android only There was a Jazz Jackrabbit canceled port for Windows phone due hard to find the original If you know more games that has been ported for mobile (Please no emulators) reply bellow.
Several Neo Geo games have been ported to iOS. I think several Metal Slug games have been ported, as well as Blazing Star. I think there are others, but I haven't been bothered to look. Older games are a pain to play on iOS without a gamepad. The touch controls just ruin the experience.
Theme Hospital has an unofficial port for android. I wouldn't really call Sonic 2 or 3 ports as they are just running in an emulator. Though supposedly Sonic 2 is getting a real port like 1 and CD.
Quite a few Neo Geo games on Android such as Blazing Stars and the Metal Slug series. There's also an unofficial demo of Metal Gear Solid on Android which is looking pretty good.
FYI Sonic 3 never made it to iOS officially. On iOS there are a lot of classic Sega titles. Streets of Rage, Columns, Gunstar Heroes etc.
Many of the classic arcade titles have been ported (Atari's Greatest Hits, Keystone Kapers (did it get an arcade release?), Pac-Man, et al) at least on Android. Of course, if you need to copy the original files, what's the difference between that game and an emulator?
All the classic dragons lair like games are out. Love them still. I rly wish blade runner would be redone.