I suppose it depends on what you mean by "land" -- For our purposes I'll define landing as putting the aircraft on the ground and decelerating to taxi speed, while meeting the other requirements of a "good landing" (shiny side up; rubber side down; aircraft, pilot, and passengers in reusable condition).
How fast can I go?
Generally you want to put the wheels on the ground at (or at least very close to) the aircraft's stall speed and then decelerate to a safe taxi speed. You can certainly force the wheels onto the ground at higher speeds, but you're still an aerial vehicle at that point and you have to bleed off the excess speed to transition to a ground (taxiing) vehicle before you can leave the runway.
As a general rule of thumb your final approach speed should be about 1.3 times stall speed for your selected landing configuration so you can get down to taxi speed reasonably quickly. Putting that into some kind of context, a normal approach speed (with full flaps) in the Piper Cherokee I fly is around ~65 knots. A no-flaps approach is ~75 knots.
Looking a little deeper, you can fly the approach as fast as you want (within reason) as long as you're comfortable doing that and confident in your ability to bleed off the extra speed with precision.
At my home field I've been chased down final by jets often enough that I know I can maintain 85+ knots until about a half-mile final, at which point I can reliably dump the extra speed, put the wheels down in the touchdown zone, and decelerate to taxi speed in time to make a "normal" turn-off. I also know that if it seems like I will need to carry more than about 85 knots by the half-mile point I'm better off telling ATC I'll go around and land after the faster traffic because I may not be able to safely decelerate and turn off the runway with enough room for the traffic behind me to land.
Keeping your speed up is really only helpful if you don't botch the landing.
What's the procedure for doing this?
The procedure is basically "Keep your speed up until short final" -- It's something you can practice with your CFI pretty easily.
If you elect to land without flaps the procedure is the same as the "no-flap landings" you should have done in training, and in most small aircraft that should be a non-event. Again, this is something you can practice with your CFI pretty easily, and it's a technique you should be familiar with in case your flap controls ever fail.
What are the consequences?
Well, the good part is you'll be helping out ATC and the traffic behind you: if you can keep your speed up ATC will be better able to maintain separation between you and the faster aircraft behind you, instead of having to send them around or vector / re-sequence them for spacing.
It's also fun to do this kind of thing occasionally, and helps keep your skills sharp.
The bad part is that any time you're not flying a "normal" approach you're accepting some additional level of risk. In this case you're also touching down faster, which means more energy to dissipate (hopefully through braking, but if something goes wrong you'll be dissipating that energy through impact, and as dvnrrs pointed out the energy you need to get rid of is proportional to the square of your velocity so the number goes up fast).
Remember that ultimately flying a fast final or touching down in an alternate (faster) configuration is a courtesy to ATC and the traffic you're mixing with.
If you're comfortable doing it everyone will appreciate your help, but if you aren't comfortable with it just fly a normal approach and let ATC know you are
unable to fly faster -- the worst thing ATC will do is ask you to go around and re-sequence you with more space next time.