I don't think the Boss RC-505 has been mentioned here yet. After trying Ableton Live, Loopy for iPad, an EHX 2880 and a Time Factor I finally ended up buying a RC-505 and haven't looked back since.
It's far from being perfect, the body is made of not-so-good-feeling plastic, some of the on-board FX are terrible, it has no decay/feedback for the loops and in general it feels like it's a bit disproportionally big... but, it's still the perfect looper for me. The things I like about it are that you get 5 totally independent loops (not 1 loop divided in 4 tracks as on the 2880), so you can have each have its own length, synced or unsynced. I also like the fact that I can see where I am in the loop, that can be handy sometimes when there's a lot going on and you can't hear stuff well anymore. Some of the oboard fx are lousy, but some are decent imho. I use the beat repeat and beat scatter ones a lot and the cool thing is, that when you use them wile overdubbing, the resulting audio replaces the old loop, so you can keep messing with the loop.
It does support multiple sets (memories as they call them), so you can even prepare a set with some loops already there, and then jump around between them (in a quantized way if you need it).
The sync works well and is pretty solid, the time stretching is ok for small tempo changes (though I rarely use it).
an example of what I do with it: