For me, whenever I'm watching the openings and endings I watch them like they are the first time I'm watching them. I don't know why that is exactly. I guess I like to take the time and appreciate the work put into them. I have no experience in making animes but I've dabbled in video editing and the work and time required to these things is not exactly small or short. I view these as part of the artwork and I've always had an appreciation for such things.
"Recklessness is the way of the young, and tolerance is the beauty of adulthood." - Nyanta (Log Horizon)
I personally adore OPs and EDs, mostly 'cuz they're usually one of the best songs on the soundtrack, and because the animation essentially amounts to a tailor-made music video.
Probably my favorite OP at the moment is Death Parade's. Mind, I've never seen the show itself (which I hear is quite psychological and nothing like what this intro leads you to believe), but damn if it ain't catchy. Just listening to it makes me wanna get up and dance like an idiot.
OP moreso than ED. Aside from PV's, my first typical impression of an anime is through their OP. Is it generic or well thought-out? Does it suit the genre? Is it coreographed well? These things kind of matter to me. If it's a quality opening and it fits I'm more apt to watch the anime because I assume that the anime has received the same qualities. It doesn't directly influence my drive to watch, or not watch an anime. But, like I said it is typically a first impression. A good ED is always nice, but never necessary. Often I'll enjoy an ending and then skip it and go straight to the next episode.
*giggles* my boyfriend skips ops and eds all the time, it always drives me insane. i'm a bit ocd in that regard though, i can't enjoy an episode completely unless i've watched it to the very end, don't ask me why. :o
OPs and EDs to me have always been pretty independent from the anime itself. If both the ending and the opening are good that's great but I've never thought of them as being fundamentally important to the quality or my enjoyment of something, especially since I tend to skip even the OP/EDs that I do enjoy most of the time. That said if they work to really set the mood like in Ergo Proxy or Monster I think it ends up being a very effective way to leave a lasting impression.
When I watch an anime I always watch the opening first then I don't watch the ending until I get to the last episode then I watch it so that case to me it looks like a play or long show. I watch it when it ends I watch the next one ( or wait a week if they are new) and when the last episode hits bam ED at it finest. If I really like the music I will download to my song pretty much for me they are important.