Is the seed everything I need to recreate a wallet? During creation of my wallet, I was given a list of 12 words ("the seed") that I scribbled somewhere.

Let's assume that I lose all my storage, everything related to my wallet -- except for the seed.

Are these 12 words enough to recreate my wallet from scratch and regain access to my bitcoins?
Yes. If you specified one, the password is also necessary (e.g Trezor). 
It's worth knowing that the seed covers everything (on Trezor at least) such as the bitcoin (and other coins) wallet, the 2fa secrets, password store etc.