Borderlands is a pretty unusual game and I have been trying to think of what other game it most reminds me of. The answer, bizarrely, is Far Cry 2.
Both games are first person shooters set in large open worlds with hostile native populations. Driving features strongly in both games. Both games have a quest driven main path but both also offer plenty of side-quests and opportunities to wander off the main path for non-linear exploration. While Far Cry 2 does not have much in the way of character progression the upgrading and maintenance of weapons is a parallel to the constant search for new weapons in Borderlands. Even the much maligned "respawning enemies" feature that everyone hated in Far Cry 2 also features in Borderlands.
I really think Borderlands resembles Far Cry 2 more than it resembles previous role playing shooters System Shock 2 and Deus Ex. Those games had strong story lines and complex role playing elements whereas as Borderlands emphasises its first person shooter side.
The only problem with this comparison is that I hated Far Cry 2 while I love Borderlands. The reasons? Well one thing that shouldn't be overlooked is that the magic of character progression solves the tedium of infinitely re-spawning mobs. Those level 3 thugs who pop up every time you leave Fyrestone are completely inconsequential at level 18. When it boils down to it though the really important difference is that the developers of Far Cry 2 went out of their way to make the game realistic, depressingly realistic. The developers of Borderlands eschewed realism in favour of cartoony fun. Far Cy 2 was depressing. Borderlands is fun.