There are almost always guidelines on pasta packages for the amount of water you should use when boiling. Sometimes I'd like to use a pot that's on the smaller side, and that got me wondering; what actually happens to pasta if you use too little water (assuming it's at least fully submerged)?
Short answer: if you stir once or twice at the beginning to prevent sticking, and all of the pasta is submerged, you can very successfully make pasta in a reasonably small quantity of water.
Here is a direct link to the Serious Eats article both of the answers above cite.
Anytime you boil a starchy food, like pasta or potatoes (or yuca :), some of the starch ends up in the water (or broth/stock) and thickens it a bit. Now when you're making a stew, you want that thickening to happen, so you use somewhat less liquid to pasta/potatoes. But generally when you're just making pasta alone, you want the pasta noodles to remain separate and you don't want any more thickening than necessary.
Also important is that if you're talking about dried pasta, the pasta needs sufficient water to rehydrate.
At the extreme, if you used just barely more water than pasta, the pasta would heat but never fully rehydrate and/or you'd end up with a sticky, underdone mass.
One of the reasons for using lots of water to cook pasta is that the temperature of the boiling water does not drop drastically when adding the pasta when it is proportioned that way...the water will just keep boiling...or reboil very fast.. however, using little water for lots of pasta...will drop the water temperature too low and then takes longer time to reboil..the result is starchy, sticky, and gummy pasta that was sitting in lukewarm water too long.. The standard for Chefs is one liter water (4Cups) per 100 g pasta (around 3 oz)...and of course salt..lots of room for the pasta not to be crowded..