Can a random player catch the snitch?

As cool as that would be, no. According to Quidditch Through the Ages, any player catching یا touching the snitch, other than the seeker, results in a foul. It's called "snitchnip".

i doubt it but that would be halarious, harrys going for the snitch he almost has it then i random beater grabs it and wins the game for the gryffendors totally stealing harry's spotlight XD

i guess they could, but I don't think they would get points.

Good question... Maybe.

I don't think so. It would probably be a penalty shot for the other team. I was actually just wondering if someone in the stands watching the game happened to catch the snitch... Hmmm.