This is a subject which has a long and occasionally controversial history, with both commercial and DIY tweaks in the dozens, (-probably the hundreds!-) being discussed at length here in the archives, as well as on many other boards and sites.
At the extreme, there are people who go do great lengths to eliminate all kinds of potential resonances both inside and outside of their gear, packing the open spaces inside with dynamat, plasticine clay and other substances, and weighting down the outsides, while setting units on multiple-layer "sandwiches" of various materials "tuned" by science, guesswork, or random experiment to get the best results.
There is hard science behind all of this, but the real science --the mathematically proven stuff-- gets VERY complex, VERY quickly. Having pored through a specialist graduate textbook on the subject, I can assure you that this is NOT something you'll want to get into unless you are already well past intro college math/physics/engineering stuff. Hard-core stuff that is not for anyone who isn't "seriously geeky"!
Which is why it is probably best to experiment with things and hear the results. If you can hear a difference and you like the difference, then keep the tweak in the system. If you can't hear a difference, or do not like the difference you hear, then take it back out.
After all, what matters most is how your system sounds to YOU.
I've found positive improvements from putting weights atop gear. Often, this means simply stacking one unit atop another, but it can also be a slab of polished stone (with felt or other material between) or, for a much classier look, a cement Buddha, like Brett a used! It's probably best not to use something that rings like a bell in the acoustic range, but otherwise any weight is fine.
Adding dampening material to the inside of a box can also help a lot. The most commonly-recommended material is "dynamat", sold for dampening sound in automobile body panels. It is a sheet of metal backed with a sticky, black tar-like stuff. You cut it to size and then stick it down tightly, making sure there are no air bubbles underneath. It's usually the best stuff, but it is both difficult and messy to remove, so use it with care. A cheaper, more easily-removable, but not quite as effective dampener can be any malleable stuff like clay, putty, blu-tac, etc... Just make sure it won't melt when warm and doesn't conduct electricity!
Consider dampening not only the inside of the outer case, but also any transformer casings and suitable areas of transport mechanisms. Adding glue or silicon caulk, etc.. to stabilize capacitors against vibration can also help. Adding extra vinyl or rubber washers to the circuit-board mountings may help (but may also be silly overkill; apply common sense first!).
As for feet, again there are the soft/rubbery type which "dampen" vibrations, sorbothane which "absorbs" vibration, and solid/hard cones, which focus the weight into tiny point areas and thus "couple" the unit to its base, allowing vibrations to be transferred through the base efficiently.
The base itself can again transmit vibrations through to the shelf or other support and to/through the structure of the rack or shelf, then the floor, to/through the structure of the building, to the Earth. Obviously, in most cases nothing noticeable will reach the level of the Earth, but the theory is there and valid. Bolting gear solidly to non-resonant pilings driven into bedrock would be ideal for a "coupling" approach, although earthquakes would create issues.
At the other extreme, floating gear on, say, air (like some air-bearing and/or magnetically-suspended TT platters) and then using layers of material like sorbothane, cork, air bladders (tennis balls, etc...) to isolate vibrations can work.
There are also approaches that "stack" or "layer" materials of increasing or decreasing density, to draw vibrations away or to trap/deplete them in areas of little effect. DIY turntable plinths are full of such experiments, many of them utilizing thin layers of softer materials between thicker layers of harder material in what is called "constrained layer damping".
People use substances like sand and lead shot in bases, because these tends to absorb vibration well. When used in speaker stands, many people recommend "tuning" the stands by experimentation, saying that TOO "dead" a stand sounds as bad as too "lively" a one. Similar views are common regarding speaker cabinets themselves, even though theoretical physics suggests that the best sound should come from the "deadest" structures.
Much of the time, what you want to do is transmute higher-frequency vibrations into lower-frequency (sub-audible) ones, by increasing the inertial mass. Adding a big weight/mass to something usually accomplishes this. Occasionally this approach can backfire, though, bringing some vibrations into audible range, so experimentation is needed.
Probably the best improvement I've had from this approach was recently, when I took a boomy-bass, mediocre-sounding pair of vintage Pioneer SE-20A headphones, and by adding some blu-tac to the backs of the driver motors, turned them into one of the best vintage cans I've heard yet. Complete sonic transformation, with just two small blobs of blu-tac applied in the right places.
It's sometimes useful to apply the "rap test" to anything in the system: rap on it with a knuckle, or tap it (gently!) with a hammer, and see if it goes "thud" or rings like a bell. Generally speaking, a dull, short and quiet "thud" is best, although there may be occasional times when you want something to 'ring'. Note the rap-test result, and a apply a consistent strategy to reduce/eliminate resonances and vibration where you don't want them, through absorption, transmission, and/or transmutation.
A very useful tool for vibration-troubleshooting is a doctor's stethoscope. It will allow you to hear noises in your gear that you cannot hear with the naked ear. Put it against all the parts/areas of your gear, and LISTEN for sounds that are transmitted. Can you hear the motor here, or there? When you rap on the shelf/base or on the case of the unit, where can you hear it? Apply the dampening tweaks and listen again, until you have minimized the noise that is audible through the stethoscope.
It's possible to use more sophisticated pick-up microphones and measurement gear to do this for frequencies your ears cannot hear but which may still affect the gear's performance and the end-resulting audio output, but this would be really obsessive overkill for anyone who isn't a professional gear designer, IMO.
In fact, all of this stuff is actually so complex in the real world, with so many interacting variables, that the best approach is simply to experiment, experiment, and experiment. But keep it fun, and don't obsess over it. Enjoy and appreciate the improvements, and laugh off the failed experiments as part of the fun. After all, it's just a hobby, and one that should be about pleasure, and the results you can get just from simple experiments can be very impressive and satisfying already.
And don't forget that sometimes, the noise you may still be hearing is coming from OUTSIDE of your system: especially if you live in a big city, and/or have a lot of 'noisy' electrical appliances in your home, then getting a dedicated power supply line for your audio gear, and an extreme isolation transformer, will probably do as much or more to quiet your system, than all the anti-vibration tweaks will.
My biggest single sonic improvement was probably when I replaced my ceiling-fan's speed controller with a variac. Completely eliminated a very annoying buzz, most noticeable across the AM radio band. But it was also dumping "noise" into the power circuitry, that only the big isolation transformer took out completely. Another noise turned out to be caused by arcing between the contacts of an electrical plug and the socket, from a lamp!
So tweak away, but remember that vibration, while important, is only part of the total picture... and always, always, HAVE FUN!
P.S. Congratulations if you made it this far. You have survived another one of the occasional Arkay "verbal diarrhea dumps"! My apologies to the poor server! 
Revelations await.
). It is light, and fairly fine, so I think it would work well. I think I noticed a difference. I will be trying some other home remedies over the next while.