Electrum (
http://electrum.org/) is a great bitcoin client. Its main advantage is not having to download the blockchain - Electrum connects (via Tor, too) to Electrum servers to determine balance. But don't let that fool you - Electrum is packed full of intelligent features to make maintenance and use very versatile. For example: in Electrum, with just a "seed" (a private hash) you can restore full duplicates of your wallet.
Give Electrum a shot; and consider hopping into #electrum on freenode IRC. I've talked to them a couple times and they were very helpful.
EDIT: in response to your OP, Electrum does not store any private keys on any server. Only you maintain the private keys, a.k.a. the control of your BTC. When using Electrum - you are still the sole responsibility over your keys.