When it's your mistake:
1. If you hit something really expensive (like an SL600), you can't afford fixing it. If the owner is a big dirty guy (believe me there are plenty of those), sell your house and fix his car. If he's a nobility, apologize and he will understand your poverty
2. If you hit a bike and the biker is not injured seriously or dead, you are lucky. You are *seriously* lucky. Pay the guy even if he is a little unreasonable. Asking him to put it on his insurance is *not fair*. Btw insurance companies do not investigate into minor claims (<1L, even more) that do not involve injuries (at least mine does not).
3. If there's crowd nearby, see the sentiment, do accordingly. Pay, negotiate, take whoever to hospital, whatever the sentiment demands. Remember, nothing is more important than your being intact and pretty.
4. If it's really dangerous to stop (crowd sentiment etc OR you are scared), go to the nearest police station and tell them the fact. Cops won't consider it hit and run if you report right away (someone pls confirm).
5. Don't give your license to anyone who's not a cop.
6. So far as possible, avoid reporting any accident that can be mutually settled to cops. It's more efficient that way. Rememer : your and the cops' time is valuable.
Having said all that, we don't live in the most civil societies in the world. People get bossy, even physically agressive. Sometimes you hit an Auto or Taxi - they all belong to their brotherhoods - can't help. Tricky, very situation dependent. No standard logic to tackle the infinite scenarios of Indian roads. Sometimes you hit a cow, you lose bumper, cow loses a leg...what can you do? All situation-dependent.
Try love, money, law - in that order. Then try their combinations.