Any legendary pokémon, the most fun thing is to capture it and use it in battle to crush all resistance like only legendary powers can. Or maybe if it's Giratina, it could be interesting if it brought me along to its world for a little sightseeing.
If I had Darkrai, then I would have it pretend to be someone's shadow and make strange poses. When they take a look at their shade and see what's happening, they would be a little freaked out. That would be quite funny, wouldn't it? If it intimidates them a bit too much though, then I would call Darkrai back into my Poké Ball. If I allowed it to keep scaring them, I'd feel kind of guilty at the end. And I'm not such a huge fan of the feeling of guilt. d: Also, if I was ever able to capture Raikou, Suicune, Entei, or one of the Swords of Justice (excluding Keldeo, since it's too small), then I'd ride it in front of my friends. I would love to see the look on the their faces—they'd be extremely jealous!
I'd love to be able to have a Mew that knew Transform, as I'm sure it could result in some funny pranks that we could pull off. Maybe I could even convince it to transform into me and make it go to work in my place. That'd be fun for at least one of us, right?