Biggest factors:
1) Resolution
2) Texture depth/detail (i.e. graphics settings or mods)
At 1920x1080 at "Very High" C3 can gobble-up 1.5-2GB easily.
At 2560x1440 or 2560x1600 at "Very High" it can cross 2GB.
At 3840x2160 or 4096x2160 (4K) at "Very High" it can break 2.5-3GB.
At 5760x1080 (triple-1080p) at "Very High" it is possible to see 3-3.5GB+.
Regarding BF3, it is a actually a fairly light game (graphics-wise) compared to more taxing games like Crysis 3 and Metro 2033/Last Light, the level of texture depth and detail even on Ultra isn't all that mind-blowing. In fact the visual differences between Medium and Ultra is so subtle that a lot of people don't even bother with Ultra. It was a game designed to appeal to large masses while still having the ability to scale and tax high-end cards.
Skyrim in particular is notorious for having people install so many freaking graphics mods that it breaks all vRAM records, I'm talking 2.5GB+ at only 1080p!
The reason cards are loaded with so much vRAM these days is because firstly it is cheap to pile vRAM chips onto the PCB, secondly it greatly helps to market the card for those who like to see big numbers (no, seriously) and thirdly because the moment a game finishes the vRAM on a card it will start to use system memory (regular RAM) to keep going...but that memory is a hell of a lot slower and you may start to see the game stutter (or even crash).
It's easy to avoid any possibility of running out of vRAM with...well, plenty of vRAM