I just read this article in BBC news about negative interest rates:
If the Bank of England cuts interest rates on Thursday could the interest paid on our savings fall below zero?
Negative interest rates, where the bank charges us to look after our savings, have been seen before.
In the 1970s Swiss banks charged foreign customers rather than paying them interest to hold their money.
I don't think we'll see negative interest rates in the UK, although it is technically possible, and has happened before. To use the hypothetical example offered by the BBC: if you place £10,000 in the bank, and the negative interest rate is at -1%, then at the end of the year you'd get a return of just £9,900 -- essentially a £100 charge for the pleasure of banking. Great.
A word of warning if this does happen: Northern Rock will, to quote one comment from the Guardian website, look like "a 6 year old emptying his piggy bank".