I've never carried an interest-bearing balance since opening my first credit card back in 2006. I do take advantage of 0% finance options when I need to (Best Buy, Google, etc.) and I always pay them off before the period ends. I have never done a balance transfer, but if the need ever arises, I wouldn't hesitate.
I try to live within my means and I've been fortunate enough to never have had a large enough life disaster to warrant carrying a credit card balance. I try to treat credit cards as cash that earns me more cash (excluding my 3 AF cards).
I don't know exactly how long I've gone without paying interest but it's very satisfying to see "0.00 interest paid year to date" on my statements
I'll be 11 years this September. 
I don't think I have ever carried a balance and paid interest on purpose. 30 years of credit cards for me. I think I was accidentally late a few times over the years but if I remember correctly, I would call and get any fees or interest reversed. When I was in my late 20s/early 30s, I did use one of those 1.9% promo rate checks to buy a used car so I did pay some interest then. And this was arguably dumb (but it worked out, lol), I used one of those low rate promo checks for part of the down payment on my current house, bought in 2008, so paid some interest there too. So, the answer to the last time I paid (low rate) interest is probably 2009, 2010 at the most.
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