The original Bitcoin software wallet is called Bitcoin QT. You have other cryptocurrencies that are using the same software. Bitcoin QT is a full Bitcoin client available for Windows, Linux and Mac. You can download it directly from Bitcoin.org and have it up and running fairly quickly.
Another software wallet that a lot of people use which is also available for Mac, Linux and Windows is called MultiBit. A real lightweight client, it is fast and it is easy to use. It is also synchronized with the network quickly.
Whenever you install a new wallet, it has to go out to the Internet and download the block chain since the beginning of time for that particular cryptocurrency. It includes every transaction that has occurred. So literally, it can take hours or days depending on Internet speed to get your wallet set up if you are using something like Bitcoin QT. MultiBit clients synchronize quicker.
The third of the “big three” of desktop wallets is Armory for Windows and Linux. It is a really advanced client that extends features and functionality. It’s mainly used by power users. It offers encryption and secure cold storage of wallets. That means you can move your wallet onto a paper that’s obviously not connected to the Internet – another way to protect and preserve your wallet.
People who have large amounts of Bitcoin should use Armory and keep most of their coins in cold storage. The obvious advantage to being on a computer that is not hooked to the Internet is that you cannot get easily hacked.