My own rule is that a character won't notice or describe himself unless:
-- He's vain.
-- He has body dysmorphic disorder or a lesser anxiety about his looks.
-- Something about him has changed, and he's studying the alteration with pride or horror or whatever.
-- He has special cause, such as his profession (model, actor) or a special occasion (getting married in five minutes -- but then I'd imagine his focus to be on his clothes and hair more than his inalterable features.)
Even given one or more of the above, I would usually not let the character do an encyclopedic review of his appearance.
I usually let characters describe other characters rather than themselves. Care is also needed here. If the describer knows the describee well, she shouldn't notice that person's features to the extent of a major catalog. The describer will probably note only a few things about a new acquaintance, too. Exceptions could be a professional evaluation, descriptions by a model recruiter or a forensic pathologist, for example.
How a character describes another character can tell more about the describer than the object. This is good.
In the novel I'm working on now, the MC doesn't get a description at all until Chapter Five, when another character meets him for the first time. Then he gets a couple lines. I'm cool with that, and so are the betas.
All that said, I don't mind detailed descriptions when they're done well. I also don't mind virtually no physical descriptions of characters, as in Jane Austen's novels.
A couple examples come to mind:
The dual opening descriptions of Scarlett O'Hara. The first is by the off-page narrator, on page one -- it gets down to the slant of Scarlett's brows and the shape of her jaw, but also relates them to aspects of Scarlett's background and character. The second is by Scarlett, as she dresses for the barbeque at Twelve Oaks: a very important occasion, since she's decided it's her last chance to steal Ashley from his fiancee. Scarlett notes her good points with a vanity so frank it seems natural and robust -- her vanity becomes a virtue, part of her startling animal vitality.
The descriptions, by the narrator, of the sisters in Little Women. You can't get franker about info-dumping than Alcott, who comes right out and says: Here's what they look like, since you readers like to know that stuff. However, her descriptions are succinct and pointed as much toward character as physical appearance.