Most people out there probably eat cooked eggs, but there’s a fringe out there of pro-raw eggers out there who idolize Rocky and say drinking eggs is super healthy. Of course, most people probably think the only real issue is salmonella, but this is far from the case. Here’s my far from complete list of pros and cons on raw eggs:
– Uncooked eggs have less digestible protein 
– Egg whites contains avidin, an anti nutrient that binds biotin. Cooking denatures avidin.
– Uncooked eggs can obviously contain more bacteria/bacterial toxins. I don’t think this is huge risk though, especially if you know your source and aren’t immunocompromised, but it can be.
– Uncooked egg whites contain a compound that inhibits trypsin , a protein digesting enzyme. This could partly explain why cooked eggs have more digestible protein.
– Uncooked eggs appear to be more allergenic  than cooked eggs.
– Cooked eggs can create oxidized cholesterol. How much depends on the intensity of cooking. Dietary oxidized cholesterol might be bad , or it might not be that bad. I’m not sure, but it’s not a good thing.
– Cooking eggs appears to decrease vitamin E content .
– Cooking eggs also appears to decrease folic acid content .
– Chris Masterjohn has written about how undenatured protein, including egg whites, may be better at increasing glutathione levels .
I eat mostly slow cooked omelets when I have eggs, but I do throw a raw yolk or two into a smoothie from time to time. I tend to shy away from raw eggs for the potential digestion issues and avidin, but they seem to have some potential benefits if that’s not a concern.