When logging into my Google Account today I was met with a suggestion from Google that I should hand over my phone number for ‘recovery’ purposes. While I’m happy to hand over most things to Google, my phone number is something I give out very selectively. As you can see password recovery is already dealt with via a secondary email address, a common solution used by a lot of online services.
Yes, this is optional, so don’t feel pressured to give up your phone number. If you consider receiving your recovery code via SMS a valuable service, then go right ahead. Naturally, if you have an Android phone, Google pretty much already has your number anyway.