Exactly how it's been undercooked is also a factor.
If you have an item that's been well-cooked on one side, without being cooked on another side, you're at a much higher chance for pathogens than something that's been well seared but still rare in the middle.
Besides what SAJ14SAJ has mentioned, you want to cook all exposed surfaces. In the case of ground meat (which exotec has mentioned) almost everything is an exposed surface, which makes it much more difficult to deal with, and you're dealing with more complicated machinery that's more difficult to clean than a simple blade.
You then have other factors, such as how it's raised, where it's been processed, how long it's been since it was cut and what temperature it was held at, etc. In general, the less time since it's been cut, the less risky it is, assuming all other things (like the cleanliness of where it was processed) being equal.
All of that being said, eating raw beef on its own is not a problem. There are plenty of places where it's still practiced. My experience has been with Ethiopean food -- kitfo is raw, ground beef with spices, while gored gored is cubed, raw beef. Inuit also eat raw meat, but it's typically frozen first, and rarely beef.
As for what might happen ... that's been pretty well covered on the bad side ... but there are also groups out there who advocate eating raw meat, or even rotting meat to help with digestive issues. I don't know that I'd personally recommend it, though.