Are there standardized ways of generating wallets from passphrases? Brainwallet is a well-known tool that lets you generate an address from a passphrase. I think Brainwallet just performs a single SHA256 hash on the passphrase to get the 256-bit private key of the address.

Is there a BIP-standard formulated for this calculation?

Now that HD wallets are making there way to become mainstream, I think it is useful to have a standard to generate an HD wallet from a passphrase. Electrum and CarbonWallet seem to already have implemented HD wallet generation from passphrase and they are using 100,000 rounds of SHA256, which sounds already a much safer process than a single round.

The original BIP0032 that defines HD wallets doesn't define a way to generate them from passphrases (and it shouldn't), so maybe it is a good idea to make a separate BIP for this purpose if it does not already exists.

I want to be able to switch between wallet apps just taking my master key with me. Or for HD wallets, f.e. use a different wallet for watching (using the public root key) than for signing.
Yes, BIP39 is one such way.

Electrum has a different, mutually incompatible way.