I put new in quotes because I use another little-known feature, "ControlMaster". Multiplexes multiple connections into one, it makes making " new" sessions instant (can also be configured to persist a bit after disconnecting). Also useful for tab-completing remote paths. It does not prompt for authentication again, though. And it's a bit annoying when the connection hands (can be solved with ssh -o close, IIRC).

My other favourite is I very often SSH with -v to figure out why the connection is hanging, you rapidly figure out if DNS is failing, the TCP connection doesn't open, it does open but no traffic flows at all or it opens and SSH negotiation starts but never finishes. You can learn a lot just from this about what is wrong.

Edit: it's already explained in the OP

You can also just kill the ssh process (say from another terminal). That way you get to keep your terminal window. And this works with everything "blocking" your terminal, not just ssh.