I use Legendary pokemon for training other pokemon. Legendary pokemon are wonderful for re-battling trainers, fighting secret base grunts and owners (especially because the base owners sometimes use Legendary pokemon themselves), and also for sweeping through the Elite Four for experience and cash.
Often I'm selective with which Legendary pokemon I use, I generally lean towards the cute ones like Manaphy, Shaymin, Mew, Jirachi, etc.. but I do like a few of the really spectacular and epic Legendary pokemon like Arceus, Girating, and Rayquaza.
However, all of this is based on playing with these pokemon for post-game purposes, I never play with Legendary pokemon in my play through teams or my competitive teams.
One thing I have been doing with Legendary pokemon lately, is I've been building them to compete in Contests. I kind of feel like that contests are the most balanced playing field for Legendary pokemon and it's really entertaining to give them move pools built around doing contests instead of fighting.
Ignoring all of the above stuff that I do with most of the Legendary pokemon, I otherwise just throw them in a PC box named "Legendary", and they generally just sit there doing nothing. I do however like collecting Legendary pokemon so I do sort of look at them as Trophies as well.
I also treat Legendary pokemon as being an unbalanced advantage. It feels wrong (to me) to use them in any competitive format or for even just completing the overall game. I don't get upset over people who do use them, because generally I try to build my teams with the intention that they might have to fight these Legendary pokemon and thus built to defeat them, but I would be uncomfortable with my self if I used them all the time, specifically for battling.