There is one special server that is a free-for-all server. You can kill anyone there at any level (except certain "safe zones").
The is one special server that is a joint realm Co-op server. On this server, all three realms work together.
These are alternate rule set servers, and most people don't play them, although many of the people that do love them. The majority are set up as Realm vs. Realm servers. Now there is the classic world which is YOUR REALM ONLY. Most of leveling up will be done here and in instanced zones, and you will never be ganked by anyone except mobs. The end game of DAoC is the player vs. player area called New Frontiers, which is a completely different area that does not connect with your homeworld area in any way. Here, you will encounter people from the other two realms. There are also battlegrounds for people leveling up to practice their RvR skills in. The bg's start at level 1, but the popular ones are 20-24 (very, very popular), 35-39 (Molvik) and 40-44 (Leirvik, least popular of the three, but sometimes okay) There is also a new bg for 45-49 people that will be starting very soon. You can gain realm ranks in these bg's, which allow you to gain added abilities or stats.