I thought this was a good quick read on the subject.
Yes, Peeves, pumps are possible without supplements.
A "pump" is (as Gun Ryo started to explain) the result of a muscle becoming engorged with blood and waste byproducts. This is a natural consequence of repeatedly and forcefully contracting a muscle. When you flex a muscle repeatedly under a load, like curling a dumbbell for 4 sets of 12 reps, the muscle produces waste products (lactic acid) which must be flushed out of the tissue. Excessive lactic acid buildup happens rapidly, and results in the burning sensation toward the end of a set. It's your body's way of shutting down what you're doing, so you don't injure yourself. Of course, this game is all about pushing that limit, and working beyond what your brain is telling you your muscles are capable of.
The rush of blood to a muscle being worked strenuously serves two main purposes: it flushes out the lactic acid, and delivers nutrients to rebuild and repair.
Typically, a pump is a short-term phenomemon, lasting only an hour or two after a workout. Supplements like Nitrix and NO-Xplode can prolong that condition through vasodilation (vaso = blood vessels, dialation = expansion). By relaxing the blood vessels in your muscles, Nitric Oxide causes you to carry a great deal of that pumped sensation over a longer period.
One last thing: while a good pump is not necessarily an indication that you had a productive workout, the inability to acquire or sustain a pump for the typical 1/2 hour to 1 hour after a workout is usually taken as a symptom of overtraining.