My comments on Qiaochu's answer are getting long so I'm going to delete them and expand them into an answer.
Simply put, Qiaochu has the right of it. I just wanted to expand on his answer a bit. :) Most of the sequences in the OEIS are indeed unimportant, and some are only barely even mathematical - consider e.g. A027887, the sequence of legal bids in Skat.
But in fact the OEIS actually includes keywords to let you know about this! Keyword "less" indicates "less interesting sequences"; there's keyword "dumb" for "unimportant sequences"; there's keyword "base" for those depending on writing the number to some specified base and keyword "word" for those dependent on the words for numbers in some language.
And if you want things really lacking in signficance, skip "dumb" and go straight to keyword "unkn", which includes things like the clearly unimportant A104101 (which hardly seems "mathematical" at all, unlike the bids in Skat, which have a pretty clear formal definition from the rules of Skat). Of course this also includes things like A078686 which may indeed be significant, just not in any way that anyone can currently discern!
I should note, I get the idea that we can to some extent distinguish "recreational" in the sense of "doesn't really relate to anything else and is hard to say much about" (e.g. A005245, to promote something I've done some work on :) ) vs. "recreational" in the sense of "has a totally arbitrary definition and probably falls under one of keywords 'base' or 'word'" (e.g. happy numbers). (Really, you'd think people would at least have the decency to work in base 2. :P Although in the case of happy numbers I guess you need at least base 5 for squaring digits to be interesting.) But the OEIS includes sequences important or unimportant alike. Now, if you want the really important ones, that's what keyword "core" is for... though this doesn't necessarily include everything you'd expect, such as the numerators of the Bernoulli numbers.
Of course, probably the main source of usefulness for the OIES is that if you are working on a problem and get a sequence of numbers you don't recognize, you can look it up there and see if you can identify it with an already known sequence. So while the OEIS certainly contains all these unimportant sequences, you're not so likely to see them unless you're doing something "unimportant" with the OEIS in the first place! I mean, unless they had a hidden significance that nobody realized till now...