Like mentioned, grab a tape delay plugin and set your delay time to 0.0ms.

If your particular DAW doesn't allow you to use 0.0 as a setting, set it to 1ms and then use the latency compensation in the track to bump it up by one millisecond to compensate.
From there it's a matter of messing with smoothing, flutter, and distortion if available in your particular plugin (in Logic, it's available in the drop-down at the bottom of the Tape Delay plugin screen). You can achieve some really wild and out there effects, or just a slight smoothing and minor attenuation of highs like what would happen if you actually were recording to tape.
Just beginning my experiments with this and used it on a track I was in the middle of trying to get a good mix on, but here's a quick example of the difference it makes even with really, REALLY modest settings:
No Tape Delay/Saturation at all.
Tape delay/saturation added to the drum bus, the bass track, and each guitar track individually. The biggest difference seems to be the drums. Cymbals really gel better with the whole mix here than they do without it. There's a tiny bit of smearing going on in the guitars that I'll need to work with to get figured out.
Overall I think this is a useful trick for those that don't have tons of cash to toss at plugins.
Feel free to jump in and add any tips you've got when it comes to recording and/or mixing.