Well, it is important to first take into account the purpose the level was built for.
If I take some level from Counter Strike and play it alone, without bots or other players, it will be a very boring experience, because there's nothing to do other than kill yourself.
Counter Strike maps were designed as arenas of sorts, so that participants would compete against each other for supremacy. Other than your opponents, there isn't anything else on the level to oppose you.
Different game modes have associated with them different purposes. So a map created for Deathmatch will not be "optimized" for a different game mode, which might ruin the experience considerably. With that said, this type of game tries to create levels in a way that removes as many uncertainties as possible (ideally), so that player skill prevails over "randomness" or "luck". At the same time, since the context of the game is the confrontation between Terrorists and Counter-Terrorists, levels are expected to resemble real-life locations in some way or another. This not being the number 1 priority though, as it could get in the way of the gameplay.
In Quake single-player, levels were created to reinforce gameplay as much as possible, which results in those levels not looking "realistic" and having no other purpose than to present obstacles and challenges for the player. Games like Mario take this approach as well (i.e. can you get to point "x" while facing all these obstacles?), with little focus on story and realism.
So, the important matter at hand is, how do you determine the quality of a level? That is, how good a level is at achieving its purpose?
Because just achieving its purpose is not enough to call it a "good" level.
After all, the most memorable levels are those that achieve their purposes masterfully.
For "arena" games, it is probably by giving the players from both sides fair means of defeating each other. If it is team based, it should allow for different strategies that work best by means of cooperation. And so on.
One level that I will never forget is this one:
The way I see, Thief was about challenging the player in obtaining something hidden somewhere. The premise was something like: "Here's this thing you have to obtain. Here's some info. You have these starting resources. Now figure it out".
But the thing is, not only it managed to create interesting objectives and obstacles, but at the same time it presented a convincing world and atmosphere -- you really felt as if you were in a real, breathing world.
The level design reinforced both gameplay and story/setting at the same time. It felt natural.
This is what games (that want to focus on story) should be like. This is what the industry should be striving for. Not this "cinematic" crap we get nowadays, that have more in common with movies than anything else.
Other than Thief, games like Shadow of the Colossus and Realms of the Haunting comes to mind. Dark Souls is also a good example, but there's is something about it that doesn't feel as natural (maybe the death-revival/monster respawn cycle?)