I have played a large variety of character, from heavy warriors, light warriors, rogues, assassins and mages, and I have noted that during all these there are some skill trees that I just never use.
Lockpicking. I swear I have never had to leave a chest locked in this game. Doesn't matter if my character is a low level warrior and it's a Master lock. I can always get it unlocked. And the perks to add treasure ... again I have never needed money in this game. By level 10 I'm the richest person in all of Skyrim.
Speech. Again, don't need more money. What few speech checks I have failed had other options anyway (entering Mages College for example).
Most other skill trees were used by one character or another.
So what skill trees do you never use and what should be done about it? Honestly I could play Skyrim without Lockpicking or Speech in the game, but I don't want them removed (heaven forbid they've removed enough already). What I'd like to see is some reason added to the game to use/need the perks in these skill trees.
For example, you can't make any armor in the game without spending perks, why not make it so that certain locks can't be picked without them. Having played TES since Arena I am all too familiar with the "You lack the skill" message for tougher locks. Somehow I lived through it. Just about anything is better than having just useless skill trees.