PuTTY is the most popular SSH client tool out there and you can even use it without installing (portable version). You can also do local, remote, or dynamic port forwarding. It gives you control over the SSH encryption key, and it uses its own format of key files. It was originally made for Windows, but it also runs on Mac and Linux machines.
It allows you to use remote machines, and it is free and open source. PuTTY is a client program for SSH, and it allows you to run a remote secure session over a network.