They are often referred to as the Holy Trinity - Healer, Tank, DPS. At the moment they are the dominant way to organize character roles in fantasy RPGs but they aren't the only way and I was doing some thinking about the consequences of removing the Trinity and replacing it with something else. The thing is that specialization is intensely powerful. We can see this in society today in that I know how to do only a tiny fraction of the jobs out there with any kind of competence and in fact a large proportion of tasks that need to be completed for everyday objects and activities are well understood by only 1 in 1000 people or less. Do you know how to make a pencil? Wire a circuit board? Make gasoline from raw oil? I sure don't, but the benefits of having a society of specialists is undeniable. The same holds true for fanasty RPGs; groups that have people that specialize as much as possible in their role are more successful at what they do. The healers and tanks don't have to do damage as long as they are as good as possible in their role of mitigating damage and the dpsers don't have to contribute in any way at all other than killing the enemies.
In order to eliminate the Trinity we would need to eliminate the way in which it works, which specifically means getting rid of the WOW type of aggro. As long as somebody can take all the damage from the monsters and mitigate it more than somebody else there will be tanks and as long as anyone can spend all their time healing there will be healers. Simply normalizing mitigation isn't even enough since as long as people have customization control they will find the best tank and make that person tank even if the difference isn't that large. What we need here is some way to swap aggro around the group with an element of randomness, remove the ability of players to be only a healer and give everybody the ability to heal themselves. Imagine that the formula for getting aggro on a random monster is
Probability of getting aggro = Monster Max Health / 4 / Attack Damage Done
and that a similar formula would be used for bosses but the 4 would be replaced with some other much larger number. The idea is that if you do at least 25% of the monster's health in a single attack you get aggro for sure and you have a proportionally less chance to get aggro by doing less damage. This means that monsters will generally be hitting people who hurt them the most but who they hit and when they change their minds is somewhat random. With this aggro formula everybody has to be able to take a hit from the monsters and nobody can reliably 'tank' them. This means that everyone has to be aware of what the enemies are doing and be ready to defend themselves in some fashion.
In order to get rid of the healer role we would need to get rid of spammable heals that can target others. Imagine that a healer only had two healing abilities that could affect other people:
Healing Aura: All healing done to players within 10 yards of you is increased by 20%.
Mend: The targetted player heals for 5% of their health every 2 seconds for 20 seconds. You may only have 1 Mend active at a time.
This would mean you could have people with healing abilities that wouldn't be 'healers'. A character with these abilities brings different things to a battle than a rogue would because they do help people heal better and can put a little bit of healing onto the person getting pounded but they have to spend most of their time using their attacks. You probably want a healer around but there is every reason to think you can succeed without one.
We would need a comprehensive set of defenses and self heals for every class for this to work but it should make group composition much less rigid. Any 5 good players should be able to beat any 5 man challenge but there would be some compositions that are better than others. It would also help pvp dramatically as everyone would have to be keeping 'how tough am I?' in mind for pve and the sorts of things that both activities demand would be more similar. A pvp focused character and a pve focused character should be much more similar and balancing them should be much easier. Would it make the game more *fun*? That is a harder question! I very much like the idea of flexible group compositions and roles and letting people do many different things depending on the encounter. I think though that the much greater role of randomness in combat would make tight tuning of pve encounters and balancing ranged and melee classes dramatically more challenging (or impossible). I think the RP elements would be better as combat would feel a lot more like movie fights or fantasy novels where the monsters don't all stand around pounding on the ridiculously tough guy who can't hurt anyone.