Good practice to use same SSH keypair on multiple machines?

To be a little more clear from the other answers here and other places: the "safety" is only as secure as the security of the private key. If someone can get access to your private key(s), it could possibly be emailed or copied to a USB device. Then the copied private key could be used by another person.

As long as the private key is in a secure system, then there is no problem having it go to multiple machines.

But one thing I will say: do not copy a private key to a remote system. Try to rely on the SSH agent (ssh-agent or pageant) and agent forwarding. If you do have a private key on a remote system, make sure that it is not the same key used to access the system.

Yes, it is safe as long as it is in safe hands i.e. physical machines are secure. Of course, if an attacker gets access and is able to ssh into one machine, he can then get the key from that machine, and use the key for other computers as well. See this for more information.