Funny to think of rabbit as an exotic thing. Though not as common in Britain as it used to be, you still get it occasionally, indeed our local butcher makes rabbit pies, which my lady and I have on a semi regular basis.
I was also surprised when I was in the states how little people over there had Indian or Arabic food, since in Britain I grew up with both, and these days curries, kebabs and Kofta are all common items over here, as well as Japanese Raman, Chinese dimsum and mexican food, plus the more standard fish and chips. the bigger problem is more one of quality, especially when you get into some of the less savory types of local takeaways.

I admit I have a bit of a texture problem with a lot of soft fruit and certain raw vegetables like tomatoes, which limits a few of the more exotic thing I can have, kiwi fruit is out for example, however I do try to try different things when I get the chance.

Some more unusual things I have tried include:
Zebra (our local pub used to  do amazing zebra meatballs), Kangaroo (a bit disappointing), frogs legs (absolutely lovely), Escargot, that is snails in shells (very nice if you like shellfish, not if you don't), ducks tongues (quite unusual and not my favourite), Squirrel (tastes rather like Liver), squid ink rizotto, more unusual for how it looked than how it tasted, deep fried ravioli nachos, which was wonderfully weird and quite nice, chicken feet, (which I was not keen on), tempora battered celery, which was really good, and even deep fried mars bars or snickers, which are sort of lik a heart attack waiting to happen .

I'm also quite keen on actual game birds, pheasant is one of my favourite roasts, and my family have had goose for Christmas several times which is nice.

Most interesting thing I've eaten was goat, which is nothing.  Takes spices well, and allot like lean beef just tougher and a bit more fibrous.

Other than that, I partly grew up on East Indian food (punjab region) so I'm pretty into that.  Stomach can't take the same level of spice now as it used to though. :-(

Yeah, goat is nice, though I've only ever had it stewed.
My lady loves fish,  so  we tend to eat a lot of fish, and of various kinds. Pollock for example is waaaay nicer than cod or haddock and is becoming a much more common thing in Britain (we just had some for dinner yesterday). I'm personally less keen on mackerel or kippers, and tuna I only tend to like if prepared correctly which it often isn't.

Mullet and munk fish are two absolute favourites of mine which are quite unusual, indeed at the same West Indian restaurant where I had the curried goat, they do an absolutely amazing monk fish  stew with muscles.

One other odd thing which I do like is  Haloumi cheese. This is a thick, rather rubbery goat cheese with a salty after taste (originating in cypress. The key thing about it though, is that it is one of the few cheeses that does not melt. This means you can have it fried, grilled, or better still barbecued, indeed these days a lot of vegetarian breakfasts are using it instead of bacon, which is good sinced its much nicer.

A friend of mine barbecued some a while ago which  was absolutely fantastic!

They better be, considering how bad yack's smell.

I found venison burgers to be really good too, although they can be a bit dry. Bison is the same, but yak is pretty good.