Which altcoins have testnets? Bitcoin can be run on a public testnet (by using a different port than the real Bitcoin network). This is very useful for development, because you can test software handling Bitcoin without handling actual value.

What is the situation for Bitcoin alternatives? Is there a testnet for most (or all) altcoins? Which altcoins have such a testnet feature?
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 :)