Does a Sengir Vampire survive when blocked by four 1/1s?
All of the creatures will deal their respective damage at the same time. Since Sengir Vampire's +1/+1 ability is a triggered ability, it uses the stack, and before any of the +1/+1 counters go onto the Vampire, it will die. 

State-based actions (like death from damage) will happen before the triggered ability on the stack can resolve.

If any of the creatures involved have first strike, however, this changes things:


If the Sengir Vamire has first strike, it will deal it's damage before the blockers, killing them before they have a chance to deal damage, giving it the +1/+1 counters
If the blockers have first strike, they deal damage to the vampire before it deals damage to them, killing the vampire while they remain alive
If all parties have first strike, the outcome is the same as if none of them did.