Assuming you would still have a line of credit, it makes plenty of sense to pay off the loan. You're paying 16 percent for money you don't need right now. Pay it all off and you can start rebuilding your savings account.
So what do you do in a future emergency? Well first off, you can use the savings will will have to fund some portion of it. The rest you can borrow again, as long as you have a line of credit somewhere. The icing on the cake though, is that once you stop carrying a balance, your credit card purchases will have grace periods again. Once that grace period kicks in, it's an effective short term free loan, and if you really wanted to, you could move money that would otherwise immediately go to purchases into savings. The difference is that you're paying in full again, and aren't charged any interest on the float. Just remember, that if you fail to pay in full by the due date, they charge retroactive interest and fees.
An alternative is to find a way to consolidate your credit card bill into a collateralized loan. HELOCs for example. The rates are much cheaper than your CC bill, but require you to have some equity in the home. One thing to consider is that HELOCs are an open line of credit that can't be easily taken away. The interest is also tax deductible, unlike your credit card interest. There's also unsecured lines of credit from banks and credit unions, and if you have the credit score the can be cheaper than credit cards.
I think I've shown here that there's plenty of alternatives to carrying credit card debt for the unexpected in life. Pay it off!