Yes. I've never had any debt, not even a mortgage. Neither has my husband. And at this point we almost certainly never will.
How we did it:
We were fortunate in that both sets of parents paid for undergrad, but we were also both exceptionally motivated and hardworking and had partial scholarships (and both of us had very good options available that we could have done debt free if we had had no support). We also come from fiscally responsible families that set a good example (my parents in particular are the millionaire next door type, though not mustachian). We've both had credit cards since 18, but neither have ever had a balance.
I worked several jobs in college, enough to fund a year abroad on my own after graduating. Both of us have STEM PhDs, which are generally fully funded and come with a stipend that is plenty to live on, even in the high cost of living areas where we were (Bay Area and Boston). I started maxing my Roth and funding a taxable account in grad school, and didn't notice a difference between what I had/did and what other students had/did. My husband worked as an engineer for several years in between MS and PhD (before we met). He bought his first new car with cash during that time, which is our only car to this day.
After PhD, I went to a relatively well, but not crazy well, paid industry job. My husband became a professor, which pays a good bit less. We bike, we cook, we've never had cable. We rented an apartment in the Boston area for a few years, then moved for his job and rented a tiny cottage. We stayed there until a few months before baby 2 was born (location was amazing, but we were starting to go insane with three people living there and me working from home most of the time).
Then we bought our house. We didn't exactly plan to pay cash, but we're pretty picky and had been looking around for a few years while putting down payment money in a savings account. So we wound up with enough in the account to pay cash somewhat unintentionally (I know this is a controversial decision, numbers-wise, but we're happy with it. And two STEM PhDs generate a firehose of money that we had to put somewhere). We never found something we loved, instead we ran out of time before baby 2 and just bought the best thing we could find, which is a fixer upper in a nice neighborhood in a relatively high cost of living area (but nowhere near as high as Boston).
At this point many people on this board would declare us FI in our 30s based just on net worth, but we don't think so just yet. Partly because we are somewhat risk averse, partly because we plan to fund at least some college as our parents did, partly because we live in a somewhat high cost of living area and like it, and partly because our spending is slightly higher that what is considered 'acceptable' around here (e.g. we have a nanny), though still low enough, especially relative to income, that everyone else probably thinks we're insane.