It would have to be something expensive, classic, and timeless. Probably a black Chanel bag large enough to carry my everyday things. I could never afford that right now, but if I was to only buy one bag and then not buy any others for years upon years, it would be something elegant like that.
My gold leather Foley + Corinna city tote. It's the most versatile bag I've ever owned, and convertible into a messenger because of the strap/fold-over design. Even though it's ginormous, I've literally worn it to the club, through the snow, with coats as well as summer dresses, and even traveled with it. I eventually had to diversify, but the city tote made me a one-bag-woman for 3 seasons.
The size is perfect be it when I just have a couple of items, or when I need to stuff papers, books and shawl. Be it when I am dressed up for lunch or running off to the supermart in a polo-shirt and skorts. Some pics attached.