It's tricky and of course context dependent. It'd be much easier if there was no apparent motive (massive debt, impending arrest, history of fraud etc). I've often thought a holiday to a developing country with porous borders would be your best bet. If you are in a western nation it's quite difficult to disappear within your own borders, and it is hard to survive without an identity. Even then, most western nations will send someone/s to investigate your disappearance or pursue the matter via Interpol etc. Add to this your appearance is likely to raise attention if you are obviously not a local (in my case I am a white AF guy with tattoos who would not melt into the background in India). Further, no matter the money you have you ultimately want some type of identity and passport in case your current situation gets hot. In my scenario I would travel to country A using my legitimate credentials, then disappear (drowning is a good one, cheers Harold). I'd then leg it to the neighbouring country (country B) where I'd attempt to get a new identity using forgeries I'd already organised from another country different to my home. Once I can establish my identity in country B (residency over months/years etc) I'd then move to my final destination and keep my head down.

There's plenty of stories of those who try to restart and get caught (Nick Rossi, John Darwin). Common thread is they don't completely break from their previous life, or they move somewhere too obvious. Another key point is having to deal with some real sketchy people to make all of this happen properly. You'd essentially need to be smuggled across borders and acquire forged documents.

I'd be keen to hear others back-of-napkin plans.