For me, a level in a game is one of the most important factors in what makes a great game. Sure you can have the coolest characters and weapons on the planet, but if the level doesn't work or make sense then what's the point. Most recent games have decent to excellent level design, it almost comes as standard, and gamers, without probably knowing it, realize just how important a game level can be. Its just as artistic as character design in my opinion.
Even though environment art isn't really my thing, I can appreciate and respect artists that can produce good environment art, and create very complex, intricate levels. Most levels in current gen action/shooter game are free roam/sandbox style where you can go where ever you want, without any restrictions. A lot of recent games also contain hardly any loading screens, which can have massive advantages in terms of game play and overall enjoyment.
Not a lot of games nowadays contain any 'invisible walls', which where quite common a few years ago. These can be disappointing to the player, as often other parts of the level can be seen and not explored. A recent game with this still apparent is god of war 3. Although I think the style of game play may make these more noticeable, seeing as it's predominately a game where you follow a set path.
In terms of design, a lot contributes to a great level. The placement of certain objects, the different effects such as fog or rain, the overall mood/atmosphere of the level etc. I would almost compare it to film set design. Because the level is 3D a lot of thought has to be taken in order to create an atheistically pleasing level from all angles. It would be no good if the front of a castle was amazing, but the interior was very low quality in comparison. Which means consistency is a very big factor when it comes to the overall design too.
When I play any game, I'm constantly trying to find secret parts of the level not normally shown to the player. I think even though this would be a very small part of a massive cake, it can still add to the overall gameplay and level exploration.