I think it would depend on where in the pack you start.  My friend who ran competitive cross country in college warned me there is a lot of pushing and shoving as people fight to get onto the trail first, and it might be like that up front.  When I ran an X-C race a couple weeks back, starting MOP, the race was really pretty civilized -- sure, there were people passing and being passed, but sans bloodshed.  (Of course, there were only about 300 people in the race, versus the 2,000-7,000 that road races in my area draw, so maybe that's why it was more civil ...)

At the start of a crowded race it can be very physical as everyone vies for the front of the pack. At D3 nationals one year there was quite a pile up, which blocked about half the field from advancing and resulted in many runners getting stepped on. Keep in mind that runners were wearing spikes and at least one runner got it in the head. He did finish the race. Even later in the race things can get heated. I saw a punch thrown after one runner grabbed another runner by the shoulder to get past. I have also seen one runner use another runner's ankle to pull himself up a very steep, muddy hill. None of this is typical. I ran probably 75 races and watched a lot more than that and rarely is there anything worse than some jostling.

Just watch out for people trying to spike you.  it could be on purpose or by accident!

Step on/Kick you intentionally (sometimes unintentionaly) with the spikes on the bottom of their shoes.

I depends on how narrow the trail is... people generally dont mean to push and shove during a race but if the trails narrow just be aware of the people around you... the worse thing that could happen is you fall (or lose depending on your goals) in which case you get up... typically i dont get pushed so much as people step on my heels or we smack arms

As others have said: it really depends on the race. If anyone has seen the start of a race a the Woodbridge Invitational in Irvine,CA they know what I'm talking about. 300 runners per race and in the first 400m the course bottlenecks so people usually get pushed and fall. Some races have a course that is nice and wide with around 100 runners so there's no need to fight for your spot. There are three ways to get around the pushing and shoving in any race though:

#1 don't race, but why would you be there if you didn't want to race right? =P

#2 get out in front and don't fall =/

#3 get in the back and just worry about not stepping on those who have fallen XD