Sync is one of the trickiest and most essential parts of the transfer and editing process. Any number of elements can cause your audio to slip out of sync and you have to be ever vigilant to keep it all in line. A common problem is sample-rate mismatch, which was addressed above. If your edit session is set at 48k samples per second and your source audio is 44.1k samples per second then you'll start to notice sync issues within a 60 second clip.
Another common source of problems is the difference between film speed (true 24 or true 30 frames per second) and video speed (23.987 fps or 29.97 fps). Some cameras have documentation or settings that state 24 or 30 fps (indicating film speed), but in reality they run at 23.987 or 29.97 (video speed). Others actually can switch from film speed to video speed. Audio recorded at 48kHz or 44.1kHz assumes that it will be run at video speed (23.987 or 29.97), so if your camera and your edit session end up at film speed then you will end up with drift until the location audio is pulled up by .1%. This difference of .1% can cause sync issues within a 3 or 4 minute clip, and after 10 minutes or so the drift can cause sync to be off by nearly a second. To avoid this most digital video projects should be shot, edited and post processed at video speed. Either 23.987 or 29.97 work great, but remember that your documentation and menu settings may be a little misleading if the manufacturer resorted to shorthand when setting up what the parameters look like.
The third and trickiest of sync issues is often created by the display that you are using itself. Modern flatscreen displays such as LCDs, plasma, and DLTs have been shown to introduce non-trivial amounts of delay in the picture. The Dell LCDs that I work on induce about 1/2 frame of delay by themselves. Further, all digital video interfaces including firewire and USB add a layer of delay into the display chain - often as much as 4 full frames. The way to deal with this is to measure the delay in your specific display chain and then offset the audio playback by the same amount. The playback tab inside of system settings in Final Cut has a field called "Frame Offset" that does exactly that. One easy way to check display sync is to set up a countdown leader that has one-frame sine wave pops that play back as the numbers change. Experiment using the frame offset until the sound and pictures line up exactly.
Its important to address sync issues early and seriously, as they can cause huge headaches if you let them get out of control. Most people can perceive sync shifts as small as 1 or 2 frames, and people are far less forgiving of sync shifts that place audio before the picture than the other way around.