Bitcoin newbie here. I recently installed the Bitcoin client, and purchased some bitcoins from Mt.Gox. My problem is that my client is constantly synchronizing. I've checked charts and seen that my Bitcoins were successfully purchased, but my client seems to be stuck "Synchronizing with network". I've just got a constant loading icon in the bottom right, and when I hover over it it says it's "catching up". As I said, I'm new. Is this normal? Can someone explain what's happening? Thanks!
This is probably normal. "Synchronizing with network" really means "downloading the block chain", and it can take a few hours to a day.
Following the "catching up" you should see the number of blocks already downloaded. At the time of this writing there are 220,000 blocks, when it reaches that you are fully synchronized. If the number keeps increasing you're probably on the right track.
You can speed it up a bit by forwarding port 8333 on your router (not very important, if you don't know how you don't need to bother).
Meni describes the issue well enough: Your Bitcoin Core is still catching up, and your incoming transaction will show up once the blocks that confirmed it get processed.
If you want to check meanwhile whether the transaction went through, you can use a blockchain explorer. Enter the address you gave when you requested the payment to see whether the transaction is visible on the network. You can find a blockchain explorer for example at blocktrail.com. Entering your address does not compromise your payment.