I live in Connecticut, so it's not the craziest place for wildlife, but I've had some interesting encounters.
To the people mentioning deer: is it really that exciting? I guess maybe they're less common in other places. I often see about 10 or 20 of them on a regular run. Yesterday I would estimate that I came across at least 40, including a herd of 21 on a golf course fairway.
As for more interesting experiences, I've had a couple. The most interesting was this past summer. I was running in the woods almost in the dark, turning onto a trail that pretty much no one runs on or knows about because it connects two main networks. This one animal started barking and running circles around me, but I'm pretty sure it wasn't a dog. It was about the size of a dog, but it ran with scurrying feet like a coyote. It also barked with the low-pitched voice of a dog, but would go into a coyote-style howl sometimes too. It was terrifying. Eventually I managed to slowly walk away after several minutes of its aggression. I didn't run through that section for a while, but after a month or two I started going through pretty often again and haven't had anything else happen. Does anyone have any idea what this thing could have been?
Interestingly, in that same section my friend had a weird confrontation with a big deer. It blocked his path about 10 feet in front of him and whenever he took one step backwards from it, it took two more towards him. Eventually it stopped following him at the same place where my dog/wolf/coyote left me alone. Weird.
Besides that, I haven't had anything too crazy. I came across a big white skunk in the middle of the road in New Haven. Also while mountain biking in New Haven, I saw a bobcat, which was pretty cool. That was around two months ago, and I just saw on Wikipedia that apparently they aren't believed to live in Connecticut anymore. But I'm pretty confident that this was a bobcat.