If someone spilled coffee on my laptop what are my rights?

It depends on how/why the coffee spilled:

1) If the person deliberately spilled it, he or she should pay for repair or replacement (if necessary--note: if there is no real damage to the laptop, then regardless of fault, there is nothing to sue for--you can't recover compensation without damage or loss).

2) If the person spilled because he or she was negligent, or unreasonably careless, then he or she should pay for repair or replacement if necessary. Unreasonable carelessness is basically doing something stupid--for example, running with a coffee cup; texting with one hand while holding coffe with the other; etc.

3) If it was just an accident without fault, or at least without this person's fault--maybe you bumped into him or her; or the Starbucks (etc.) was so crowded it was hard to walk through and someone jostled the person; the person slipped on some spilled liquids; etc.--then the person does not owe you anything. Without fault, there is no liability.