By "Bitcoin Core" alternatives I mean full validating clients that follow consensus rules (do not fork the blockchain... because that would be an altcoin).

The ones I know are:

Bitcoin Knots: This is developed by Luke Dash Jr and has some experimental features that sometimes are added into the Core client: https://github.com/bitcoinknots/bitcoin
Libbitcoin: I think this one was founded by Amir Taaki: https://github.com/libbitcoin/libbitcoin
BTCD: This one doesn't have a wallet and is written in Go: https://github.com/btcsuite/btcd
BitcoinJ: Very old client from back in the day, I think it was started by Mike Hearn: https://github.com/bitcoinj/bitcoinj (removed because not a full validating node)
Bitcore: Looks like Trezor uses this one, but also Bloq...: https://bitcore.io/
Bcoin: Some exchanges use this one like Bitwala: http://bcoin.io/
Gocoin: Written in Go: https://github.com/piotrnar/gocoin

Im sure there are more.. post yours. I think these efforts are good and positive for Bitcoin overall. As long as they follow consensus rules, it's good that several different teams are working on different clients.