Sustain is not that difficult to achieve, as per my experience. Two things you can do are:

1. Allow for a generous amount of high gain in the higher frequency range early on in the signal path of the preamp stages. You get this by using frequency selective networks, like the "Marshall" 470pF bypassing a series 470K resistor, etc.

Then you need to dump some highs to ground at the end of the preamp, otherwise the sound will be fizzy, buzzy, eerr... shitty. This will result in a lot of compression, and you will end up with something akin to a Boogie type of sound... Is this what you want?

2. Build some controlled instability into the amp. This is done by careful placement of the lead dress, and you would have for example the output (plate) connections of the last stage close to the grid wire of an earlier stage in phase with that (so, count two stages back, or 4, or 6, etc.). Thisis a very tough balancing act, but it can be done, more often than not by accident!

If you're modifying a Fender amp, for example, chances are that if you build two more stages of gain in there, you will end up with a whistling amplifier because it will tend to oscillate easily. The reason is the wires will cross back and forth because the layout of a Fender chassis was not made to acommodate high gain signals... Anyway, when you begin to address the lead dress issue in those amps, at some point -- if you do things right -- you will get rid of the whistling sound, and that's the point where you have to start playing with the instability factor to make the amp "be on the verge." 

While that eventually tends to work fine -- I went through all of that with a SFDR -- the amp will sound great at lower volumes, because you will get nicey, chimey feedback effortlessly. However, when you take the amp to a gig, where you will be playing it al loud volumes, you may find that you will have a hard time keeping the amp under control because it will tend to take off on you without a warning.

For what it's worth, most of the guys that achieve a lot of sustain -- for some reason, Santana comes to mind :) -- to do not by necessarily having a lot of gain in their sound, but by playing their amps brutally loud and positioning themselves accordingly on stage. Both Santana and Gary Moore, for instance, mark the "crucial spots" on stage during sound check.

If you get any amp, say a small Deluxe Reverb, and dime it... stand close to it, and chances are you will find a proper orientation where the guitar will feedback like a mutha. Of course, hotter pickups will help, as will having a semihollowbody, as will playing on the bridge pickup (i.e., more high end). The advantage of this method is that the amp doesn't have to sound super processed or distorted to get the singing to happen. The downside, it is a very hard thing to do consistently.

3. Buy a used Boogie, they can be had for around $500 and if you get a IIC+ or an early Mark III, you will have an amp that sings great IF you dial it is properly -- these amp will not crunch like a Marshall though. :)

Gil 

In some of the other responses high volume and a sweet spot were mentioned. It's good to note here that there is sustain type feedback which essentially keeps the same note and the other kind of feedback which goes up an octave, then another etc. The type you want will change the route you take. If you want the increasing pitch variety remove the negative feedback loop from your amp. either by turning up the presence control or by increasing the feedback resistor some. 

if you want the same note type sustain, (it doesn't get higher) keep the NFB loop in the amp and crank the volume. Now this might not always get you there. Other things are available to help, the single biggest in my mind is using cathode bias instead of fixed. This makes quite a difference. There are two sides to the compressor thing, raising the quiet notes and lowering the loudest. Lowering the loudest won't help much here so I won't suggest a tube rectifier, but the cathode bias certainly does raise the quiet ones. 

I think this is interesting. As far as I can tell the following have been touted from time to time as contributing to the overall sustain of a guitar:

1. Mark mentioned good guitar acoustical properties.

2. Keep seeing products which add headstock weight.

3. enorton mentioned neck thru body. Can I generalize to good neck to body connection?

4. heft of guitar

5. big frets

6. brass bridges and nuts were big at one time

7. Mark mentioned pickups make a difference

8. amp feedback, special place on the floor

Any opinions on the truth or fiction of any of these claims? No baggage, really. Just curious what other people have observed. 

I would generally agree with that list. To expand on "good guitar acoustical properties":

a. Wood type, quality, and density (where higher quality and density equate to better sustain)

b. String gauge (thicker=more sustain)

c. Action (higher action=more sustain)

d. String angle off saddle and nut. The angle formed by the string when crossing the nut (or saddle) is very important. The greater this angle, the better the sustain--this is why fender uses string trees, and also the reason behind tilt back headstocks (ie, Gibson, and Carvin guitars).

e. Neck stiffness also increases sustain. This is why more sustain is to be had from neck-thru-body, and set-in neck designs than from bolt-on necks; this is also why some guitar makers add graphite reinforcement rods to their necks.

Sustain can be increased in two ways (ignoring electronics): increasing the energy of string vibration (ie, thicker strings); and decreasing damping of vibration (ie, stiffer neck, denser body wood, etc...)

Here's a cool little trick: remove the bridge, scrape off the finish that lies under the bridge (you should mask off the surrounding area for the duration of this process to avoid unsightly marring of the surrounding finish) until you're down to bare wood, use a very fine pin to poke a bunch of small holes in the wood, and SOAK the area with crazy glue (cyanoacrylate). When it dries completely sand the surface flat and flush with the rest of the guitar top, and remount the bridge. The crazy glue dries hard as a rock and improves the energy transfer from the strings to the body, thus increasing sustain (it also seriously strengthens the area). I've done this to several guitars--its pretty quick and easy, and I've gotten good results.