chessparov said:
3) Try dynamic microphones or ribbon microphones on vocals.
4) Use a more "musical" sounding parametric EQ
Here's a good analogy: Digital recording is very accurate. Imagine your original sound source as having some blemishes or zits on it's face. When recording to analog tape, the interaction of the magnetic particles, particularly when saturated, can have a very mild airbrush effect on some of the blemishes.
In my opinion this effect is greatly exaggerated, because I've heard a lot of analog recordings that lacked just as much warmth as anything tracked purely digital.
Chessparov's suggestions are really good ones. A lot of cheaper condensers tend to have a somewhat metalic sound to them, that digital recording isn't going to do much to hide/cover up. Ditto on the EQ. Good dynamic mics running in to good, accurate preamps can sound very smooth and rounded (ditto on the ribbons, though I have limited experience with them). Example:
A Shure SM7 or
an Electrovoice RE20 in to a Grace Design or similar lower-impedence solid state pre (The RNP, or Alan's new pres might be worth a look as well).
On guitars, be wary of your amp tone. If you're using a POD or similar amp modeler, then don't expect the same lush sound you'll get with a dynamic mic pointed at the grill of a Vox or a Mesa.
Be wary of your room accoustics, as a lot of early reflections and/or nodes will just plain sound bad, period. And certainly nowhere close to "warm."
If you just like the sound of tubes, ala 60's, Revolver, etc. Then I'd look at the prospect of investing in some good tube gear. There's not much "real" tube stuff that can be had on the cheap, though, so be sure this is the sound you're after before you go sinking a lot of money in to it.