For example:
USA
EB5 investor visa: $1,000,000 or $500,000 depending on the area you 'invest' in. One of the easiest ways to get a green card, and from there, citizenship
UK
Tier 1 investor visa: £1,000,000 in 'investment', which can just be the purchase of government bonds. Apply for indefinate leave to remain (green card equivilant) after 4 years. If you invested £5 million, you only need 3 years. If you invested £10 million, it is down to 2 years. The UK non-domicile tax status can also be very very generous to wealthy expats (unless they are American and thus are taxed on world wide income regardless).
Canada
Canada used to have such a program (Immigrant Investor visa for $800,000 CAD for people with net worths of at least $!.6 million), but that was terminated recently. I believe the Quebec version is still open though