According to themoneysavingexpert.com (a great website to check out) this will answer your question if you bank in the UK - and I'm guessing you do, based on your username and avatar.
I've copied this directly from Martin's Money Tips weekly mailout:
The £35,000 protection golden rule. For all bank &
building society deposit accounts, eg savings, cash ISAs, fixed
savings, in the unlikely event a bank goes bust, £35,000 per person,
per institution (either an individual bank or a banking group) is
guaranteed. While the PM plans to raise it to £50,000, that ISN’T law
yet. So if you’ve over £35,000, spreading savings helps mitigate any
risk.
I've copied this directly from Martin's Money Tips weekly mailout:
The £35,000 protection golden rule. For all bank &
building society deposit accounts, eg savings, cash ISAs, fixed
savings, in the unlikely event a bank goes bust, £35,000 per person,
per institution (either an individual bank or a banking group) is
guaranteed. While the PM plans to raise it to £50,000, that ISN’T law
yet. So if you’ve over £35,000, spreading savings helps mitigate any
risk.
