Most OS X users don't use "ssh GUIs" because OS X ships with a very good Terminal application. This is unlike Windows where the cmd.exe or even a PowerShell are not friendly command line interfaces to remote servers.
In OS X, you can just fire up Terminal.app and ssh from the command line with:
You can use a more advanced terminal application like iTerm2 and it will allow you to save "profiles" that, when called up, automatically run a set of commands in the terminal for you. You can use these to automatically start ssh connections (which can be interactive terminal sessions or stunnels):
You can start and stop stunnels from the command line as well -- after all, these are just ssh connections that open a local port and forward requests to a remote server. For example:
ssh -f firstname.lastname@example.org -L 2000:personal-server.com:25 -N
And you're done.
Private key authentication schemes are supported by the ssh command line that ships, default, with any OS X version.