If you suck riding off road, you will also suck riding off road in Mongolia.

I don't know what wild animals there are in Mongolia... It seems pretty empty.

That said, when I was travelling through some parts of Africa than had lots of lions and such, I was afraid to camp. Campers get attacked from time to time there. But in Mongolia? What is there in Mongolia to worry about?

There are bears and very hungry wolves, given the emptiness. For nomadic Mongolians wolves are a major concern, since they tend to attack their animals during the night. This is why most of them have dogs that keep an eye on things at night time.

[The following was added on 07 Sept 2012]
I have just found this new information on the net and I am publishing it here just to add and complete the topic:

Mongolia has 136 mammal species almost 400 different types of birds and 76 species of fish. From the abundance of wolves to the globally endangered snow leopard, there is a myriad of wildlife to track, photograph and hunt. The central and northern forest area is home to wolf, wild boar, elk, roedeer and brown bear. Steppes and forest margins support marmot, muskrat, fox., steppe fox and sable. Western high Altai Mountain boasts a rich varied wildlife. Apart from common wolf and wild cats such as lynx and snow leopard, Altai is home to the world's largest wild sheep-argali and Siberian Ibex. The Gobi desert and the eastern Mongolian steppe are inhabited by thousands of gazelles. The rarest animal in Mongolia- the Gobi bear is found in the south western part of the Gobi. Wild ass and wild camels are abundantly found in the desert while Argali and Gobi Ibex also inhabit the rocky mountains within the Gobi region.
Wild horses have been reintroduced to the country from captivity abroad after being unseen for about thirty years in their dome country.
Bird life is rich and includes the golden eagle, bearded vulture and other birds of prey.
Eastern Mongolia is beginning to have a shy but considerable population of Siberian tigers, which cross the border from Eastern Russia (where their number is rising consistently) into China and Mongolia. Some Siberian tigers have been found as far South as South of the Gobi Desert in China.

Just caught up with this post again.

Water: I happily drank from village wells and water supplies without boiling it and with nil effects. Yes there is a risk but I don't think it is high (although years ago I caught hepatitus a in Nepal from following this policy - so sometimes there is a downside). From my perspective i hate the litter and waste that bottled water and canned drinks bring so I am ready to make this trade-off.

Wild animals: Yes always a possibility, but I think very low probability. For most of us the dogs that the locals use to guard their flocks are more of a risk than any wild predator. I certainly would not camp near a local yurt unless I had agreement for that reason. I camped most nights and had no issues other than at one sight where the chomping noise made by the local gerbils as they munched the grass through the night was impressively loud. (And as an aside its hard to predict which animals are dangerous. A kangaroo came sideways out of the scrub and landed on my front wheel, when I was doing 80 km/hr the other day and took me out - that was a lot more dangerous than any other wild animal I've ever dealt with)

Its very easy to worry about too many things when preparing for these trips ( I know I do sometimes) but for 99% of travellers it is not the dramatic stuff such as wild animals, robbers or the like that will cause problems, it is the simple things like a flat tyre, broken bike or the rest. I think it is best to simply do the best prep you can in learning your way around your bike and learning a little (even a few words) of the language, the history and culture of where you are going - then get out and enjoy.