Which altcoins have testnets?
Most mine-able coins are essentially clones of the bitcoin code and therefore have testnet. Many alt-coins do not have very active testnets so finding another peer on this network can take time, but given enough patience, your alt-coin testnet node will find another connection. 

If you are impatient you can google for "testnet addnode" and include the coin you are looking for; this will (hopefully) find forum posts of people who have setup/found the IP address of a testnet in your desired coin, adding this to your configuration file will make your client attempt to connect to this IP on startup. If you need help with a particular coin, let me know :)