Home insurance — what's actually worth claiming for?

Just renewed my home insurance and it got me thinking — in 4 years of homeownership I've never actually claimed. The excess is £250 and I'm terrified that making a claim will spike my premiums.

What have people actually claimed for? Is it true that claims push your premiums up for 5 years? At what point is it worth claiming vs just paying out of pocket?

Also — do I actually need accidental damage cover or is it a waste of money?