I remember plenty of numbers. The ones I dialed in the 90s. Friends I haven't seen for 20 years, who no longer live in the same country - I know their number. My phone number I had from when I was 6-10? Yup.
My landline number now? No idea. I use it a lot (no real cell coverage at home)
Yeah that's why I figure it'd have to be something fairly important - most people should at least know their area's emergency number, and hopefully at least one close friend/spouse/partner/parents to help you out. In the states we carry a paper with our insurance info which will include a tow company if you have towing insurance.
I mean, I know enough numbers by heart to get myself out of a rough situation and my phone is unusable.
Generally, I would recommend most people at least commit one or two to memory. Enough to pass a message along to your wider network or to get assistance.
My landline number now? No idea. I use it a lot (no real cell coverage at home)