The Players' Guide to the Cities/Leveling
When you acquire enough experience to reach a new level, your combat level will automatically increase. However, before you can choose new powers or assume any of the other perks of an increased level, you must first visit a trainer. Trainers are scattered throughout Paragon City and the Rogue Isles.
In addition to being able to add a power at every even level (through Level 32), there are other advantages that you gain as your character advances. You get additional slots for enhancements (received at every level without a new power slot), additional slots for inspirations, and the ability to select a title, as well as special perks like the ability to enter new secure zones, the ability to start a super group (at Level 10), or the ability to take a sidekick/lackey (also at 10).
A complete list of benefits gained when you train for each successive level can be seen here: Leveling Chart.