So, are you getting regular clicks or just a click when you hit play? If you're getting regular clicks are they at regular intervals, or randomly throughout? Do they correspond with the splices or are they somewhere else? Does this happen with all your looped material? If so, what kind of looped material - audio, midi, apple loops? Does it happen when you solo non looped material?
Clicks when you hit play can occur because Logic has a bug where it "finishes out" the sound, including reverb tails, from when you last stopped the playback. If you play for a second in an empty part of the track until the project is silent, before you play or bounce from a different point, you won't get this.
If clicks are happening more randomly throughout the track, it might be something iLife has done with your audio driver. As simple as your buffer being turned down too low, or something more complicated like a need to reinstall the driver for your audio interface.
Hope that gets some wheels turning..