I like medium steaks, but I'd never eat an undercooked burger. The reason even rare steaks are safe to eat is because e.coli and all that only live on the outside. Cook the outside for 10 seconds or whatever, and that's all gone. But when you have ground beef, what was the outside is now all over the place. It's just not safe to eat a bloody hamburger.
Eh, there's levels of safeness. i wouldn't recommend eating a burger like that from Applebees. i've done that a few times, and despite the fact it's delicious, i get a mildly upset stomach afterwards. But if you go to a restaurant with a good reputation, i really don't see the harm in it.
If you make your own ground meat, it's generally safer. Just take equal amounts of cubed sirloin and chuck, toss them in a blender, then tap blend a few times until they have a kinda ground meat consisency. Usually that's about 10-15 times. Add a dash of salt and mix them together. Cook as usual. Next time i do this, i'll probably add some lamb to the mix for that nice mild gaminess.