@pufy, while it is not possible to send dogecoins to a normal Bitcoin address because the address would not be valid,
it is possible to send dogecoins to a multisig Bitcoin address, the kind that starts with a "3". That is because Bitcoin and Dogecoin have multisig addresses that are interchangeable.
What happens when you send dogecoins to a Bitcoin address?
Please note that you are not really sending the coins to a Bitcoin address -- you are still sending them to a Dogecoin address. The real problem is that the wallet that generated the address is a
Bitcoin wallet and does not access the
Dogecoin blockchain.
Are there other cryptocurrencies that have this problem?
Yes, Litecoin multisig addresses area also interchangeable with Dogecoin and Bitcoin. In addition, there are several altcoins that even have interchangeable
normal addresses. Example:
https://bitcointalksearch.org/topic/accidentally-sent-litecoin-to-electrum-bitcoin-wallet-1554373How do you recover dogecoins sent to a Bitcoin address?
The only way to recover the coins is to ask the owner of the Bitcoin address to get a Dogecoin wallet and import the private keys from the Bitcoin wallet. Then they can access the dogecoins and return them to you. Please note that in the Dogecoin/Bitcoin case, these addresses are multisig, so the process is actually more complicated. This solution works in most (if not all) cases. As long as the generation of the addresses for each coin is the same, you can recover your coins. If the address generation is different, then the coins are lost forever.
If you want to convert/exchange one kind of coin for another, you can use an exchange or a service such as
https://shapeshift.io