Can you always eat raw meat (wild) as long as it is fresh?
Depending on what you mean by "can you eat it" you can eat anything really, it just depends on how much worse off you want to be afterward.
According to this article, dangers include:
trichinelliosis - from eating meat of a carnivorous animal
brucellosis - can be had from raw caribou
e. coli, and salmonella are rampant
tapeworm - and other worms are fairly common in fish. In fact, all Sushi sold in the United States legally must be frozen before it can be served.
For raw wild meat (assuming fresh)
Note: Most mammals can get rabies. If an animal is showing symptoms of rabies, don't eat it.
Pork & Rabbit -- Just don't. They get stuff that will kill you just from contact with an open scratch.
Birds -- While safe if cooked, most birds harbor lots of nastiness when raw. No way would I even think of trying this.
Fish -- It's extremely unlikely that you just happen to be trained in how to clean fish without contaminating the meat (ala sushi chef). If you are, feel free to nom as long as there are no skin lesions, but know that there are many parasites you can get which use fish as part of their reproductive cycle.
My rule is don't eat wild raw meat, cook it when you can't be sure both it and the preparation are sanitary. The only exception is fish caught from a line when I'm able to cleanly sashimi a species known to be generally safe when healthy.
I'm looking at you toro and maguro (tuna), sake (salmon) and hamachi (yellowtail). The salmon and yellowtail are safer if frozen first due to tapeworm and other infectious parasites - so in the wild, those get cooked too in most instances.
Caveat: My comments are relevant in the UK:
I think if your use of 'fresh' means you killed it, so you can have some confidence in its health before death and could get a reasonable view of the surrounding environment (e.g. don't eat the deer that just came out of the nuclear waste dumping site...), then yes. But make sure you cleanly gut the animal, as diseases like salmonella and e.coli are likely to be present in the gut.
I wouldn't try this with shellfish or any animal that concentrates poisons, but in general I think you'll be fine with the usual game.
Of course, if you have poached the deer from an estate, you may still be at risk from the gamekeeper :-)