I use digital for the convenience aspect of it, but sometimes I take a picture and can't help thinking that the soft, slightly "faded", washed-out look would be nice. How would I go about getting such an effect in post-processing, and what (if any) in-camera settings are required to do a good job?
The answer you don't like - out of all the digitally added film effects I've tried (and I've tried many along with actually shooting film) none really come close. That is not a scientific type of knowledge, but rather an impression. So if you really really want film look, you'll end up shooting film and even then, you'll most probably be disappointed on how far your results are from the film icons.
In many cases what is perceived as the film effect is not just a film effect, but photographer's creative vision put into right film choice and shooting technique plus the specifics of the emulsion plus photographer's editing. Harald Mante's Kodachromes are worlds apart from Steve McCurry's Kodachromes (again, personal impression based on the books, can't provide a reference).
The answer you might find useful - Nik Software's Color Efex Pro plugin contains many color film emulations and their Silver Efex Pro contains B&W film emulations. Other than that, DXO FilmPack also has pretty decent choice of films. These are the ones I've tried myself and can recommend, although this is not a guarantee of realistic rendering. Based on just web examples, Alien Skin Software's Exposure also looks interesting (I'm looking forward to try out their Kodachrome emulation).
If you use Lightroom, there are any number of presets you can use to achieve film-like effects; this is probably the easiest way to achieve what you want. Have a look here
Additionally, the film grain tool in Lightroom adds grain to photos to make them look more film-like.
There are numerous filters and special lens systems that allow you to create special effects in-camera. One of the best known is Lensbaby, a specialized lens system that makes it possible to create all kinds of effects. Beyond Lensbaby, there are soft-focus filters that can help to soften a shot, while slight over exposure can produce the washed-out effect.
I would look into advanced filter systems like Lee (my personal preference as they have glass, which is better for digital), Cokin, etc. Both brands offer a very broad range of filters for their multi-filter holder systems. Several of their offerings are special effects filters, like softening filters.
As for film grain, which is another effect of film that many find desirable and beneficial to their shots...all you can do there is use post processing. Lightroom 3 offers an explicit "film grain" tool that can add nice, fairly realistic film grain to a digital shot.
If you have Photoshop, there are lots of ways to get to the more film-like look from the old days in post-processing. Some of these have been turned into actions and The Photo Argus has a nice roundup of some good ones. In terms of camera settings, some of which can also be done post, white balance and correct exposure is the primary starting point. I'd recommend shooting RAW as well, though I always recommend that. :)