While it's tempting to list sharks, that's not true. The swimming is first in the race, so you won't be exhausted. This is done to cut way down on drowning. So if you drown during a triathlon, you probably shouldn't have been there to begin with.

Water wings are totally cool to bring, right? (Source)

You're more likely to suffer from repetitive muscle strain from the swimming. Depending on the length of the race and the temperature of the water, hypothermia can be a danger, too (source). That's why you're wearing the wetsuit. It's not just a fashion statement. A terrible, terrible fashion statement.

Biking adds other dangers. Collisions can cut you up, break any bone you can list, or just dump you on your head, so you better be wearing that helmet. You're not wearing any other pads, though, because you just climbed out of the water. If you get taken out, you're going to get hurt.

Any danger you encounter with running will be present. Shin splints and pressure fractures are both possible injuries. Ankle injuries, from twists to sprains to breaks, are also prevalent.