Most exciting wildlife encounters:
Here in the Netherlands:
Red fox, multiple occasions. Usually at a distance, one time it was right next to me a startled and ran away. Very cool to see such a shy animal so close!
Wild boar, multiple occasions. You always need to be careful when you spot them, because they live in groups and can get very upset and annoyed and can harm you. I usually keep my distance as soon as I spot them, but it's happened once I accidentally ended up in the middle of a large group with juveniles. That was scary, because I could not see the parents in the thick brush all around me. One time I encountered a lone tiny piglet, which was also scary because somewhere near me must have been the mom.
Red deer, twice. Once I saw a few does standing near the path when I was hiking in a forest. I was on the phone and didn't even realize it until they stood next to me and fled away. The other time was at twilight when I encountered a huge male that was rubbing against a tree, making a lot of noise. Scary! I wish I would see red deer more often, but they are very elusive.
Roe deer, often. I love it every time I see them, it always remains special. There was a small family that lived near me, a doe and her offspring. She had two fawns that grew up, and later one fawn.

I now live near another small family of three deer, that I sonetimes see grazing and playing in the meadows.
Brown hare, often. But like roe deer, it's always special to see them. There are many living here. The bushes next to my apartment are a popular hiding place. They are often crossing the street or wandering through the meadows.
Marten, once. At night when I was walking the dog, a marten started crossing the street, saw me, stood on his hind legs, and ran back to the bushes it appeared from.
And a great many waterfowl and other wading bird species, such as a plethora of ducks, coots, grebes, geese, herons, storks, swans. Also predator birds such as hawks and buzzards, kites, sparrow hawks, kestrels, and owls. There are ospreys living near us, but haven't seen them yet. There are lots of crows, magpies, rooks. Ravens are rare. And rare birds such as lapwings, gruttos, curlews, oystercatchers, redshanks, are quite abundant here, so they are protected species.
In Sweden:
Moose, twice. I saw a juvenile standing in a meadow some ways off. And a huge adult crossed the road right in front of our car!

Incredible. Dangerous, too.