Liu Bei: great idea.
I'd want most "rare" creatures to just kind of wander around Skyrim. They wouldn't be level-based, some might have certain conditions to when they show up, but others don't, and I wouldn't want any to be random. Mostly, they'd wander around Skyrim in the less traveled areas. They wouldn't "patrol" they'd just go around randomly. In order to find where they are, you'd have to hunt them down, find tracks in the snow, see dead animals that they might have killed, talk to people in town about them; reported sightings. Things like that.
All of them should drop some type of trophy too, like their head or a claw or something significant. Weapons and armor, meh, maybe for just one of them. The real reward is finding them.
It's all about the thrill of the hunt.
Totally agree, except for maybe a single exception with a story.
I'd like to see a variety of rare creatures: some that you find by quest, others that you can only stumble upon, some that are elusive and run, some that hide, some that perch in trees (if possible), some that lair in caves, some that hunt you if you enter their territory, etc.
In general, animals shouldn't carry loot. A couple of gold that a rat swallowed is fine, but nothing more.
A couple exceptions would be fine. For example, you've finally found the Great Golden Elk of legend. Wait, what's that? It's got an axe buried in it's shoulder, and it looks really pissed off. Or: you're getting info from villagers about a local Sabre-Tooth story, and you hear about a famous bow-hunter had just passed through asking the same questions. When you kill the cat, you find a Wood Elf arm and a single glove of Bow Mastery. But too much of this would dilute the experience and feel formulaic.