Can you get a decent return on savings in Ireland?

A big problem is inflation. It is still at near record levels, so that means that your savings are unlikely to make a return in 'real' or inflation-adjusted terms.
Deposits in Irish banks are currently at record levels, but interest rates are still on the floor. So what can you do if you have money to save? Where can you get a decent return?
While it is always a good idea to have a rainy day fund, one of the best ways to save money is to simply pay off any debt you might have.