You probably won't find more disagreement on a fantasy baseball topic than this. And I'm not just talking about verbal disagreement - I'm talking about what people actually do at the draft table.
I've seen Mariano Rivera and in previous years, Eric Gagne, go in the second round of my 15-team mixed league. And there have been people like me who have waited until round 10 or 11 to draft my first closer, usually someone like Bob Wickman or Joe Borowski.
Maybe this is coincidence, but in that league, I've always done best getting one guy (in past years, it was Francisco Cordero) in the sixth or seventh round, and maybe one more in the 10th or 11th. Sometimes, I'll draft a closer-in-waiting type for my reserve roster, and usually during the season, there are players to pick up.
But I don't buy the cavalier attitude that people have who say: "Don't ever pay for saves, it's only one category, and there are plenty of guys on the waiver wire to pick up."
First off, if your league is competitive enough to win while getting a 1 in a category, then fine, you can punt, and you'll probably do well in Ks and Wins as a result. But you had better have a good offense and not a terrible ERA and WHIP while you're at it - something that's tough to do with nine starters (who on average are worse than relievers in those categories).
And if you don't think you're punting because it's so easy to pick up a closer, think again. While Otsuka, Borowski, Saito and others were great finds last year - there are 14 other teams in my league bidding on those guys, and I might end up getting Howry or Wheeler or Burgos or some other reliever who seemed to have the job, but didn't keep it.
Plus, if you go all starters, you'll likely be behind in saves by the time you do plug the hole and will likely have to trade for them anyway, i.e., you'd hate to pick up a couple closers who cost you wins and Ks, and only gain three points in saves.
The bottom line is you have a choice:
(1) In a tight enough league where you can win despite being last in one category, you can punt saves altogether.
(2) Or you can draft/buy closers in such a way that give you the most saves for your money.
If you do (2), there's no perfect time to do it, and it varies by league (in a 4 x 4 NL only league, closers are legit. second round picks), or in a yahoo league which requires two relievers, you have to bump them up a bit.
Again, my best success rate (which is admittedly anecdotal) is when I draft a decent closer a couple rounds after the initial run (this year that would be a guy like Huston Street) and then follow that up with a sketchier guy like Jason Isringhausen a few rounds later.
One other note - Scott Pianowski made a good point on my radio show about bumping up closers with one obvious backup, e.g., a guy like Gagne who has Otsuka is safer than another sketchy closer who has no clear cut backup to get.