I don't hate level systems, but after recently playing though KOTOR2, I started to become itchy about them. (Admittedly, this isn't the first time I've thought about the problem.)
The essential problem with a level based system is the huge gulf between "high-level" and "low-level" characters. The difference between a level 1 fighter and a level 20 fighter isn't the difference between a trained but novice swordsman and an expert veteran swordsman, it's the difference between a human and a demigod.
Now, that's not *all* bad--but I do think that the curve is too steep. Even five levels of difference is enough that the lower level character cannot credibly help the higher level character. Even an entire army of level 1 fighters can't bring down a level 20 fighter.
Of course, that's partially how it's meant to be--this is a heroic game, after all. But at the same time, it presents a problem in how to handle "levelling up". Creatures that were threats at lower levels cease to become threats at higher levels, unless you use a *significant* amount of effort to beef them up.
Of course, this was most obvious to me in KOTOR2. Why? Because the *story* was much more important than the level of the characters. The fights scale to match your party, sort of. But they do tend to be on the underpowered side. But why is that the case? Well, part of it is that the party level at a given point in the plot is very difficult to predict--is this person a "do all the sidequests" type, or a "follow the plot straight through" type?
In a P&P game, the DM has control here. Theoretically, the DM is empowered to adjust the difficulty of all encounters so that they have you on edge. But even a very good DM can misestimate this--in the campaign I play in, we like a good fight, but we also tend to spend a fair amount of time not fighting. We average one combat encounter a session (we meet once a week for six hours or so.) In our campaign, the DM tends to give us encounters that are too weak, simply because we rarely have to pull out all the stops. And because he tends to believe that verisimilitude is important, he's more likely to try to throw large groups of less powerful creatures at us than small groups of very powerful creatures. In any case, a very good DM will "fudge" things as necessary to bring about the right sense of tension for the group. Too easy? Change the number of hitpoints the creatures have behind the scenes. Still too easy? Have a couple of beefed up monster types ready to roll into the encounter late. Too hard? Let the enemies drop a bit more easily, but never so easy that the players realize you're doing it.
So a good DM can adjust encounters to be appropriate to the characters. (Likewise for non-combat skill things, like knowledge or diplomacy. Diplomacy gets *really* hard for characters with a lot of skill, though, until you rule zero the tables.)
Some people might be saying at this point "well, but you can just slow down the rate of XP gain, etc. etc." You *can* do that, and we've been considering it, because the DM is unsure about taking us into epic levels (which we might expect to happen some time the middle of this summer.) But, there's a countervailing force here--and likewise, this is the reason that KOTOR2 has trouble with levels--which is the players' desire to have new neat stuff to be able to do. In both KOTOR2 and our campaign, what's really happening is that as our characters level up, the entire universe becomes tougher to meet us. Why? Because of this pressure for new neat stuff to play with.
For my own (monk/rogue) character, I don't really care about the increased attack bonus and saving throws--those are just bookkeeping--what I like is having a neat new tactic to apply. Or a new ability that I can tie in to my character's background. These special features add a greater feeling of having a lot of options, even though you're still pretty constrained to only using a few of those abilities in any one go. Like I said, in our campaign we rarely pull out all the stops. When we do, it's tremendous fun. When we don't, it's fun to try to apply the best tactics to the situation that we can.
In any case, the trouble for us is: we want new toys, but in the process of getting new toys we become closer and closer to becoming superhuman. Not because we want to be ubermensch, but because that's how things work--you level up, you get toys, you get these other things.
So what it comes down to for me is this: I don't think there should be such an enormous power differential between "high level" and "low level" characters. Unless really special circumstances apply, I think a mob of commoners should have a good chance to take down the most powerful knight in the realm. But at the same time, that knight should have a huge knowledge of tactics, etc. etc. while the commoners have good old fashioned torches, pitchforks, and big rocks.
I guess in a way, this is what people think of when they talk about "gritty". And it sort of applies here. In any case, I'd favor a more fluid system where a character can develop a greater number of options, or a greater specialization in just a few options, or a mixture of both. And while some mixes will always end up being "better" mechanically than others, they should all be workable. I think that D&D 3E (and 3.5E) has done this remarkably well, while keeping the old school (and kind of fun) level mechanic. But I also think that there is *lots* of room in the world for systems like DP9's Silhouette Core, where you don't have this additional idea of "level" that instantly separates the merely competent from the superheroes. Not that you can't go to huge lengths in such systems and end up with the same kind of difficult power curve--but I think that by smoothing things out, there's more room to experiment. You don't *need* to level up to gain a new skill, technique, whatever. All you need to do is have some free XP and spend it. And the weaker the new thing, the cheaper it is.
So--if you want a world where the best of the best are like giants among men, a level based system like D&D is great. (And fun!)
But at the same time, if you need a change of pace, a non-level based system might be worth looking at for a while. (My model for "power" for this kind of setup is that the greatest runner in the world might *still* always beat anybody else who competes with him, but a skilled novice who trains hard for a year ought to be able to get into the upper ranks. That is: it's less about time spent in the field, and more about dedication. A veteran always has polish that a newcomer can't match, but the difference in level between the rank amateur and the dedicated new guy should be much much larger than the difference between the dedicated new guy and the veteran.)
End of rant, which doesn't contain much hating, I think, but should shed some light on why there's a desire to adventure using a non-level-based system.