As well as fighting the computer controlled monsters and characters you can also choose to directly fight with other players. Fighting against other players is often a lot more dangerous because they can also use spells and prayers. Also watch out because their friends could be lurking behind a tree ready to finish you off!
Killing other players can potentially give great rewards if they are holding valuable items. However attacking another player sets your alignment to 'evil', and a skull appears above your head to indicate this. As longer as your player is marked with a skull the risk is greater. If you die you will drop everything you are holding (you won't get to keep your 3 best items like you normally do!). If you play for 20 minutes without attacking anyone, the skull will disappear and the 3 item protection will work again.
Not everybody likes fighting other players, so to do it you have to go to a special area of the map known as 'the wilderness'. Reaching the wilderness is easy, just keep on walking north and eventually you will get there. The wilderness is a desolate area full of death and danger. As well as the extra risk of attack from other players there are also many nasty monsters. However the rewards are also greater, and there is more treasure to be found if you dare to enter this area.
When you enter the wilderness an icon at the bottom right of the screen will appear to remind you. This also indicates how far into the wilderness you have gone. The further north you go the more dangerous the wilderness becomes. At the south edge of the wilderness you can only fight with players who are a very similar level to yourself, wheras as you go north you the range allowed increases, and by the north edge players of vastly different abilities can engage in combat and the danger is great!