On this one I'm totally with Vurt. Sorry Kingston!
You have to ask yourself what is more important: recording a great performance or performing a great recording. I know very few musicians who can play in as inspired a fashion if they record one at a time rather than all at once, but i suppose it depends on the style of music. I'd certainly hate to hear a jazz recording done one musician at a time, although there have been some novelty albums where one musician has played all the instruments (I think Keith Jarrett did one) which were done obviously one at a time.
In most pop/rock projects, at the very least you should record the rhythm section all at once with a reference vocal. Then you can overdub final lead vocals, backing vox, guitar solos, strings, horns, etc. later. You can record bass, guitars, and keys direct to avoid bleeding into drums, or put their amps in a different room or a closet. Have the vocalist in a different room - line of sight isn't usually critical - send them up to the attic or someplace with a long mic cord and headphone amp.
The bottom line is, in most styles, the vast majority of great music was NOT recorded one track at a time. Recording that way eliminates any chance to utilize the inherent musical talent of the performers to have spontaneous interplay and inspiration. Chances are the results will reflect that by being somewhat sterile.
Fear of bleed is over-rated anyway. So what if a little guitar gets into the bass track, or some bass in with the drums. Check some of the threads where that "accidently" happened that have been posted here recently - most of the times the poster expressed surprise at how much "better' or "more natural" those tracks sounded! If bleed is so evil, no live recordings would ever get made.
In the end it's gotta be all about the music. You can't expect musicians to compromise their playing just so the engineer can have an "easier' time when it comes to the mix. That's definitely putting the cart before the horse.