In no particular order, the shouts I use the most are:
Clear Skies
Kyne's Peace
Slow Time
Disarm
Become Ethereal
The other ones have their uses too, but with my current character the ones I listed are the most helpful. I love Clear Skies for the same reason BarnabyJones does, I just like to have nice weather.

I use it especially a lot at the College of Winterhold and in Riften. Just about all night every night, the northern lights are out in force at the College, but you can't see them because it's always snowy. And the constant fog that shrouds Riften is depressing. It's a much more cheerful city when the sun is out.

I use Kyne's Peace a lot because, at level 55, with all of my combat skills maxed, there's just no reason to engage in combat with every single bear, wolf, saber cat etc. So as soon as I see them, I just shout at them and suddenly they turn into nice little teddy bears.
Since I'm a mage, slow time has less of a good effect for me in a combat way, since once my magicka is gone, it's gone, and with Impact there's no real benefit to using the shout for combat purposes. I use that shout to get OUT of combat that I don't want to be in, lol.
Fully charged Disarm is just great. No longer need to fear those bandit chiefs or draugrs death overlords without their weapons!

Become Ethereal is good for many things. I use it most often for travel purposes. Instead of taking the long way down a mountain, I just become ethereal and jump off. Whoopee! It's also nice for getting out of combat, too.