Electrum is an open source project, it is not a company. Even if all the volunteers working on the project right now decided to abandon the project, the wallet is all open source so anyone can pick up where they left off.
It is not possible for "Electrum wallet service" to no longer be available because anyone can run the Electrum server that Electrum requires. The 12 recovery words by itself are sufficient to recover all your funds. You will either need to connect to an Electrum server in order to do so or run you own Electrum server. Even if that's not an option for whatever reason, you could also regenerate all your private keys from the electrum seed and import them into any other wallet.
This is a good answer to the Electrum example, but I assume OP wanted to know what would happen if it was let's say Coinbase that was shutting down. – Cedric Martens – 2017-12-23T20:28:59.770
As Cedric says, Electrum is an example. I simply want to know what steps I have to take to recover my funds should the unthinkable happen. By the way, if it is possible to recover my funds in a new wallet, does that mean we have a method to transfer for free? – elmclose – 2017-12-24T11:55:35.280
If the wallet provider is not open source, then you will need to trust that the wallet provider is a) secure and b) will act honestly and return your funds when they shut down. There is no blanket answer since there are many wallet providers and the above questions are hard to answer for any single wallet provider. – kaykurokawa – 2017-12-24T20:37:22.657
Just noticed a real case: Mulitbit is no longer supported. I actually have some funds in there! I am now panicking! – elmclose – 2017-12-24T20:41:43.913
Found this guide by Multibit.org people which answered all my questions: https://youtu.be/E-KcY6KUVnY
– elmclose – 2017-12-24T22:17:51.007