You can either import the keys into an eWallet that allows for that, or try taking your wallet to someone else who has a fully synchronised Bitcoin client. If you replace their wallet with yours (remember to make a backup!), the client should synchronise your wallet with the network and you will see your transactions. You can take the updated wallet.dat file back with you and use it until your Bitcoin synchronises.
Both of those options carry risk - in the first case you entrust the safety of your Bitcoins to a third party, and in the second case - to your friend. The risk could be mitigated (for example, encrypting your wallet will still let it be synchronised, but the private keys will be safer), but should always be kept in mind.
You can use any online wallet service that lets you import private keys. – David Schwartz – 2012-10-20T00:22:39.723
Version 0.7.1 of the Bitcoin.org client supports a new approach to manually downloading and then importing blockchain data, through bittorrent. And version 0.7.0 introduced -loadblock. Those still won't make the load instantaneous but will at least be faster than the normal P2P network method. – Stephen Gornick – 2012-10-21T18:54:49.673
Also, ultraprune (and LevelDB) is coming in an upcoming release of the Bitcoin.org client which will dramatically improve the initial blockchain download process and subsequent ongoing verification. – Stephen Gornick – 2012-10-21T18:56:15.117
1A a follow up to @StephenGornick, here is a torrent for a bootstrap.dat that will get you upto block 197,000: Torrent info hash: 0bb0521942f586ed96203c6f4d136324756f8a9a Torrent magnet link: magnet:?xt=urn:btih:0bb0521942f586ed96203c6f4d136324756f8a9a&dn=bootstrap.dat
Filename: bootstrap.dat Byte size: 2491771562 SHA1: e70ca90775dfdb13fd0014425805a0bdf4a31677 SHA256: a3f258e7af030165360596e4cb0b9beb24b4ce97352c22e65349b89ad5fc5d3e – Streblo – 2012-10-21T19:33:52.470