(Adding another answer rather than updating the community wiki answer, as it would involve changing most of what's there, and it may well be historically useful.)
What public test-networks exist and what are their conditions?
- ROPSTEN (Revived, following spam attacks) - Proof Of Work
- KOVAN - Proof Of Authority (Parity only)
- RINKEBY - Clique Consensus (Geth only)
What are the connection data?
Either specify the network using the ID (
3 = Ropsten,
4 = Rinkeby) or using the
--networkid value Network identifier (integer, 1=Frontier, 2=Morden (disused), 3=Ropsten, 4=Rinkeby) (default: 1)
--testnet Ropsten network: pre-configured proof-of-work test network
--chain CHAIN Specify the blockchain type. CHAIN may be either a
JSON chain specification file or olympic, frontier,
homestead, mainnet, morden, ropsten, classic, expanse,
testnet, kovan or dev (default: homestead).
How often (if so) are they reset?
- Ropsten has been live for 241 days (as of 19 Jul 2017).
- Kovan has been live for 139 days.
- Rinkeby has been live for 98 days.
Does a public faucet exist for this test network?
Does a block explorer exist for this test network?
How frequent/ reliable are new blocks mined?
- Ropsten block time = usually sub-30 seconds
- Kovan block time = seems to be sub-10 seconds
- Rinkeby block time = 15 seconds (by definition?)
Any thing else user should know about this test network?
Don't assign value to test ether.