But some character descriptions annoy or bore me. I don't really care if the person has long, slender fingers or soft brown eyes. That doesn't tell me anything about what the person is really like. Also, some writers talk on and on about their character because they think he's fascinating, but I don't think so until he actually does something fascinating.
But readers appreciate some description so they can see the character in their mind's eye. So definitely do describe your character; just keep this important point in mind:
Keep it in the context of the story.
How the viewpoint character sees the main character may not be what your character is really like underneath but if that's what other people see, it may be the best way to introduce him. Then let readers find out what he's truly like as the story goes on.
Maybe the viewpoint character is your main character. In that case, what about him is important to him? He's not going to psychoanalyse himself for the benefit of the readers because, as far as he knows, they don't even exist. Instead, include the familiar, everyday aspects he carries with him consciously and subconsciously. Think about yourself. What about yourself would you know if you never looked in the mirror?
If your main character is a trifle vain, physical attributes will most probably show up in his self-description because he will probably be a bit preoccupied with them. They will be what he considers his best traits—things like lots of hair, a well-shaped nose, or a good figure. They'll probably also be specific. And if he's vain, he'll probably notice other people's bad traits much more than someone who isn't.
He has to see the world in the context of himself. The world might look very different through someone else's eyes, and what it looks like will tell you a lot about that person--it will tell you the sorts of things that really matter about your character. You may not have to describe him much at all.