There was something I read a while ago about how if you have a mortgage outstanding the bank will keep documents relating to it (maybe the deeds) safe, and as soon as you pay it off the bank has no further interest so you have to deal with that. That particular article suggested getting your mortgage down to a trivial size and then paying off as little as possible for the rest of the term.
In some areas you can claim a tax deduction on your mortgage but I think I'd rather not pay interest, than pay interest and get some percentage of it back as a tax deduction.
If you can access offset mortgages, where you maintain a savings account linked to your mortgage and only pay interest on the amount of your mortgage that exceeds your offset savings, it is potentially useful to have instant access to what's effectively a big credit line that costs nothing unless you use it.
There's a lot to be said for not having to worry about a large monthly payment, every month, regardless of what else is going on that month.