I was raised around animals. My mom has always been a dog breeder, starting with Shar Pei, then dachsunds, english bulldogs and now french bulldogs. Of course we've had a few cats, but were never able to enjoy them as much as the dogs.
For the relatively unusual pets, we've had goats, parakeets, amazon greys, over 150 chickens and... um.. ducks, and one Transylvanian Naked Neck (known to us as a Turken, looks like a tiny turkey-chicken hybrid. really cool, but awoke paralyzed from the long neck down one day and died about a week later).
On the exotic side of things, we've had 2 green winged macaws, 1 blue and gold, 1 scarlet and a few love birds. We've had very bad luck with about 3 bearded dragons and a fat tailed gecko. The dragons all died mysterious and unrelated deaths and the fat-tailed gecko somehow escaped. Also, we've had a red-footed tortoise and a russian tortoise. A raccoon got to the Russian tortoise... I've caught many snakes, including a banded watersnake, plenty of cornsnakes and an indigo, but I quickly released them all (the rare indigo into a nearby preservation) except for the banded watersnake, which died of gluttony. It really shouldn't have tried to eat that fish, but it must have died a happy death. We had an alligator in our pond for about a year, but it wouldn't leave so we had to get someone to catch it. That was real fun, holding a wild gator is an experience. Once it was relocated, a few other gators would stop by every once in a while. My brother now has some extremely exotic and some poisonous centipedes, while I have a rare (though not endangered) Cape Gopher Snake.
Everyone says that the strangest pets we've had were the 3 skunks. 2 were pets, but we had to give them up. The other one was a severely neglected and abused skunk that had been found barely alive in a trash bag on the side of the road. We held it for a while until someone we knew had the time to rehabilitate and take care of it.
Now... I've been looking at all sorts of cool animals that I can bring in to my family, none of which I have any serious plans to obtain. Just dreaming. Electric eels, raccoons, opossums... They all are awesome, but it's a hyena which i've had my eye on for well over a year. That will be a decision I make when I'm retired, and have acres of land to spare.