"I have N years of experience in X!"
I've always been bothered by this phrase, since people obviously imply that having a certain number of years of experience in a given area must mean that their proficiency is proportional to said number of years. In most cases, it's practically an anti-signal for actual competence.
In my personal experience, the most egregious offenders are weekend golfers. Your typical weekend hacker with terrible mechanics and no course management is likely to say, "I've been playing this game for 20 years!" suggesting his supposed expertise at some point in the round. (Curiously, or perhaps naturally, the better players rarely make such statements) I wonder if these players actually know that they are terrible at the game (or at the very least are playing terribly at that time, and need to use their N years of playing poorly to prop themselves up in the face of embarrassment.
Virtually every job description you will see from traditional companies will ask for "N years of experience". This is the case for both technical areas like engineering (5 years of Java, 3 years of Ruby on Rails, 3 years of Verilog, etc.) and non technical areas like marketing (10 years of product marketing experience, 5 years of web product management experience, etc.).
Of course, this phenomenon is a side effect of the current broken state of recruiting. When a thousand people spam your Monster.com job posting, HR departments are coerced into using automated filters on resumes, which in turn promote the use of such "N years" based requirements. The fact that there are a small but significant number of excellent candidates who don't meet the exact criteria doesn't seem to matter . If the cost of getting rid of the 900 genuinely unqualified candidates is passing over 20 great ones who don't fit the bill on paper, it seems to be a cost most HR departments are willing to accept. There must be a way to fix this sad state of affairs, since as we stand today, both sides of the table lose out.
(On the other hand, requirements along the lines of "experience actually shipping web applications" or "experience creating go-to-market strategies for hand held consumer products" does seem reasonable to me.)
Teacher compensation and retention based on seniority is an enormous point of contention that I don't want to get into here. I'm definitely not qualified to say to what extent teaching ability improves over the years. All I know is that some teachers, are terrible, some are decent, and others are truly wonderful and can be life-changers for children and young adults.
But I do think that teaching is an area where having a great number of years under your belt can help, in that your sample size of students, teaching methods and crisis handling is bound to be greater. That, while correlated with teaching "ability" to some extent, I think is a distinct factor that does increase with the number of years served . So if the absolute quantity of "knowledge" in something or a concrete number of "things" one has experienced is pertinent to a role, then "N years of experience" may actually be an acceptable metric. (Though frankly, I'm hard pressed to give other areas where years of experience automatically impart relevant information like this.)
There are some cases (like job searches) where you really have no choice but to flaunt your 10 years of underwater snake charming experience. Sometimes you're in a position where you have to play the game, even though you know that the game is silly. If you find yourself in such a situation, go for it by all means, but try to maintain a certain cynicism about the whole charade.
If you ever hear me say "I have N years of experience" in anything, please do me a favor and call me out on it, so that I don't become "that guy".
 Of course, we can't forget about those job postings which ask for N number of years of using technology X when said technology has not existed for N years. (ex: Asking for 7 years of Rails experience when Rails had only existed for 6 years. Yes, this really did happen.)
 This thought was inspired by this post by aroberge on Hackernews.