It depends for me, as well. Of course with viewing new titles, I'll watch both OP and ED themes all the way through several times, to get a feel for everything and decide whether or not I like the songs and animation. Afterwards, the deciding factors are:
(1) If I like the song. I'm a big music freak, especially when it comes to pairing music with movies. So if the vocal has a good voice and the music is something to my tastes, I'll watch it every time. I never like the "kiddy" songs, the annoyingly upbeat songs with super-fast vocals that are pitched too high.
(2) How much time I have, or similar variables. Sometimes I'll squeeze an episode or two in late at night (say 2am) and therefore cannot blast the sound; or before making dinner, and in that case I'm rushing, so I will skip the themes (usually) in order to assure I see the entire episode before I have to stop the disc.
On the other hand, if I have all the time in the world, I will let the songs play out, whether I like them or not. As
ashenfairy said, it's a good chance to do something else before a new episode starts. This is especially useful if you need a potty break! (LOL)
(3) The company I keep. If I'm viewing the anime with someone else, I almost always skip the OPs/EDs after the first viewing. If I pick up a vibe that the other person enjoyed the song, I will ask if I should skip first. But most of the time, others don't get into the songs as much as I do, so even if it's a theme I personally love to death, I skip them out of courtesy.
(4) Animation. If it has a cool sequence, or just a favorite character, I'll watch it for the additional footage. I do get an excited fangirl tingle when you see Schwarz in the
WK OP, or the Frost Brothers in
GX!
There are some I dislike, though, and refuse to watch for any reason. For instance,
Berserk is one of my favorites, but both the OP and ED are horrible! I skip them so fast the DVD doesn't know what hit it!
And since others listed some of their favorites, here are a few of mine:
"Velvet Underworld"
Weiß kreuz 1st OP
VO: Weiß
"No Reason"
Weiß kreuz Verbrechen and Strafe OP
VO: Weiß
"Dreams"
Gundam X 1st OP
VO: ROmantic Mode
"Resolution"
Gundam X 2nd OP
VO: ROmantic Mode
"Gin-iro HORIZON"
Gundam X 3rd ED
VO: Nakase Satomi
"Message No. 9"
Gasaraki OP
VO: Tane Tomoko
"Dear My Best Friend"
Ushio and Tora 1st ED
VO: Sasaki Nozomu
"ex Dream"
X -Ekkusu- OP
VO: Myuuji
"Just Communication"
Gundam Wing 1st OP
VO: Two-Mix
"Rhythm Emotion"
Gundam Wing 2nd OP
VO: Two-Mix
"White Reflection"
Gundam Wing Endless Waltz ED
VO: Two-Mix
"Eden"
Yami no Matsuei OP
VO: TO DESTINATION
... I'm sure I've heard others, but those are what pop into my head right now. I should dig out my CD collection sometime; I bet I'll find a ton more since, like I said, I am a music freak!
