There are some benefits to keeping it, not the least of which is the comfort of having plenty of cash on hand (though this really isn't an issue for long since you're knocking off such a big monthly expense). Due to how stupid the system is, paying it'll probably also negatively affect your credit score a bit. So long as you have good job security, though, you can always use it for a HELoC (rates are similar to traditional mortgage and you can lock in at a fixed rate) if you should want to, and while you don't, you're saving all that cash you'd otherwise be sending to The Void in interest and fees while also being able to really build your savings/retirement by knocking what I'm guessing was a ~$1k/mo bill.
Way more important than savings rate vs. mortgage interest is mortgage interest vs. inflation (at least in the US, where the savings rate is practically 0%). It's probably one of the best times in history to get a fixed-rate mortgage (and pretty much any cheap debt you can get your hands on) in the US, but that doesn't mean it's a good time to get or keep/refinance a mortgage for you. Inflation/Fed rates have been astoundingly low, which has to eventually change, likely quite significantly where your debt is devaluing significantly faster than the interest rates you can lock into today with you having access to savings rates >0%. Of course, right now, you could use all these different "accelerated checking" schemes (credit unions in particular are good for this, but they're always named something different) which actually pay decent interest (~5% annually) if you jump through a bunch of hoops (generally, something like ACH deposit 1-3 times [Paypal] and use your debit card 5-12 times [Amazon Prime membership will do you well, here, though Meritline can be a great choice, too]), and they usually have maximum deposit limits of $5k-25k.
With or without the mortgage, there are all sorts of different ways to play it -- you have tons of options open -- go have a nice dinner and burn your mortgage papers up if you haven't already.
Important to note, too -- there's nothing wrong with being safe... if you're happy with where you are, all you're really doing each day you work is decreasing the amount of time until you can retire.