What skills only use the main-hand for damage calculations?
The behavior of some skills to use only main hand damage was decided by Blizzard since the beta patch 13 so players wouldn't have to time attacks for higher damage (by using skills right after weaker weapon had been used). If you want to read the notes, the Blizzard link doesn't work any more but I found a copy at Incgamers.
I'm not going to try and provide a list of skills; instead I will quote Bashiok (Blizzard CM):
as far as I'm aware, "certain skills" is actually just any skill that uses weapon damage as a factor.
Interestingly, someone created a thread on battle.net about this very recently - I agree with stormcontrol's post there that spammable skills without CD alternate damage, while others don't.
Thanks for asking this question, it was an eye-opener since I had a very different impression on the rarity of skills using only the main hand for damage.