What you're most likely to find everyday are not beers that are flat, exactly, but are very low in carbonation. Barleywine ale is one of these styles, and though it will typically have some carbonation, it will be very little. In the UK, real (or cask) ale is another style with very little carbonation.
The only style I can think of off the top of my head that is really and truly uncarbonated are the super high alcohol beers like Boston Beer's Samuel Adams Utopias and some of the various high-alcohol freeze-distilled* varieties. To me, these styles have nearly as much in common with fortified wine or spirits as they do with beer, and they're not easy to find, so they're a bit of an outlier.
*Distillation requires heat, so the process of freezing to concentrate alcohol in a beer isn't really technically distillation, but hey, that's what it's called, so when it Rome...