When you think “rent to own” if you're at all money-savvy you know that this translates to “expensive.” These kinds of stores make their money by marketing the “just $15/month” that ends up costing a small fortune over the cost of the rental period.
I know that there are some homeowners that wished they had rented a little longer before buying — especially if their property values fell enough to put their mortgages underwater! If this is the case, then they generally can't take advantage of lower mortgage rates because they can't refinance. Further, they're stuck with their house now. Had they been renting, they could move more easily — basically when their lease is up for renewal.
On a smaller scale, renting a piece of equipment that you don't expect to use regularly can save you money as well. Our church rented a cherry picker for a month when we needed to fix up the front of the church. We pitched in to help while the equipment was there, and could return it on time. Or, if you're planning an anniversary party then it may be better to rent the party items like the china, serving trays, the portable PA system, the tents, etc.
One-time uses are perfect candidates for renting vs. buying. It not only reduces the cost, it reduces the amount of stuff you accumulate as well!