VA: no down payment and no monthly mortgage insurance for those who qualify, with a one-time funding fee that many disabled veterans do not pay.
FHA: as little as 3.5% down from a 580 score, with mortgage insurance paid up front and monthly.
Conventional: some programs need as little as 3% down. Below 20% down you pay PMI, but it can come off later. USDA loans are a fourth kind, with $0 down in areas the USDA counts as rural.