I own an Efika and am running MorphOS 3.7 on it. Web browsing is not an option as OWB will eat up all your RAM. Mind you you could use a classic Amiga web browser, but don't expect much.
Netsurf is out of the question due to ixemul.library issues.
That aside, IRC is fine, FTP, e-mail, etc. All that can be pulled off without issue.
Odamex runs fine, but don't expect to be able to play very advanced DOOM wads with it or your frame rate will drop.
Quake II runs like a wet dream as do many other game from that era and back.
ScummVM, Giana's Return, and so forth, all run great!
Emulation isn't much of an option beyond NES and Sega Master System.
Classic Amiga programs still run like they are on crack, so it is a good means to run classic apps, though with your graphics programs still expect screen garbage with some...
...an old MoprhOS issues I could never quite resolve no matter what computer or GFX card I tried.
All in all, if you can grab one for CHEAP, it is a fun toy to have around, otherwise if you are going to dump $100 or more into it and MorphOS, might as well buy a tower system as I was not impressed with my Mac Mini experience even with 64Mb vRAM.
EDIT: I just read that 3.7 broke something so that Quake II won't run for anyone. I've not tested it my self though...