Today's cell phones almost exclusively use Lithium-Ion (or Li-Ion) batteries, which are, generally speaking, a vast improvement over the older, nickel-based varieties. Li-Ions have a high energy density, lose energy very slowly in periods of disuse, and don't suffer from what's often termed the "memory effect"--a phenomenon where, in the process of being partially recharged, nickel-based batteries will 'remember' an increasingly lower charge capacity.
Not all Li-Ion batteries are the same, however. Differences in materials and construction have a significant effect on power capacity and efficiency, and a better battery can translate to a surprisingly significant increase in the life of your device. Even the best Li-Ions, however, do lose a very slight amount of energy (30-60 seconds worth) with each charge.
Lithium ion Polymer (Li-Pol) batteries have grown in popularity in consumer electronics (and can be found in many Apple devices), but their significantly higher cost-to-energy ratio compared to standard Lithium Ions have kept them from general industry acceptance.