Three people so far pointed out the biggest problems I have with this idea, but I'm unique! T-T
Immortality would scare the shit out of me until I got a handle on identity theft and forgery. One car wreck and you have government officials wondering about your miraculous escape from injury/impossible recovery. You'd have to run from town to town every 15 years or so and cut contacts with friends, coworkers, and anyone else that gives enough of a shit about you to wonder why you don't have nasolabial lines yet.
I see two options here: powerless and invisible, or powerful and invisible.
Either be the shadow lord of a multinational corporation and buy up some mercs to cover any information leaks, or live from apartment to apartment, country to country, keeping just enough cash to bribe the right officials.
If life gets boring after constantly running from town to town, set up yer corporation or vice versa. The ever-changing sameness of humanity ensures that you'll have things to learn for a while yet, but not an overwhelming amount.
Non serious answer? Well, I'd spend 30 years practicing the Kama Sutra and own the night as THE CROWD-PLEASING BISEXUAL GENTLEMAN. On my off days, I'll rescue people from burning buildings and defuse bombs. Just remember, no capes!
TL;DR: Immortality without superpowers is hella dangerous. If it wasn't, I'd be getting laid and defusing bombs for a living.