I also suggest inputs.io
That's not a wallet. That's an uninsured, unregulated, un-audited bank account. Anyone who tells you otherwise is misleading you.
That's not a wallet. That's a bank account. Don't let anyone tell you differently.
If you don't have the private key, then you don't have the bitcoins. It's as simple as that. You have generously given away your bitcoins to a complete stranger based on a promise that they've given you that they will send those bitcoins anywhere you like anytime you like whenever you ask them to.
Imagine. You're walking down the street with $1000 in your pocket. You come to a corner where someone has set up a folding table and put out a sign printed on a piece of cardboard. You're curious so you ask them what they're doing. They explain to you that they are operating a corner bank. They tell you that if you give them all the cash in your pocket, they will hold on to it for you. Then at any time in the future, you can just ask them to spend it for you and they will deliver the cash wherever you like. They are not insured by the FDIC (or anyone else). They do not go through any sort of audit or submit to any oversight. You are not allowed to know how much total cash they are holding right now.
Do you hand them your $1000 and walk away, hoping that they'll still be there with their folding table tomorrow when you come back to ask for some of that cash to be sent somewhere? If not, why would you do the same with your bitcoins?
I would suggest you use blockchain.info
That's a wallet. That's a good suggestion for small quantities that you want easy access to from anywhere.
While I suggest you to use MultiBit which is simple and is small in size.
That's also a wallet. That's a good suggestion if you don't have a lot of storage space in your computer and you don't want to maintain the complete blockchain.
1. bitcoin.qt
Also a wallet. That one is known as the "reference client" and acts as a full node on the bitcoin network. It uses 20 Gigabytes of space on your computer.
