Spears - personally my choice, and my decision to play an Argonian has a bit to do with that, admittedly. To me, any Fantasy RPG that lacks spears seems to miss the point of armed combat, which is putting something sharp in your opponent without risking your own neck more than you have to, which is totally the point of the basic spear. Of course I wouldn't mind seeing halberds make a return as well (especially if they count for cutting weapons this time around) but my focus is on the sharp pointies.
Separate Eastern Swords - another one that confused me in Oblivion. For so long there's these widely available curved blades, and then suddenly the only ones you can find are, what, shipped over from Akavir? What are they even made of? Steel, or something else?
Melee Staff - I kind of expect this one to get the most votes, since probably about a third of TES players prefer playing dedicated magic users, and not being able to whack someone with your staff when you've run out of other options kind of takes away from the entire experience.
Flail - This would have to be my second choice. Flails are awesome, and even better would be fighting with one completely at the mercy of the game's physics engine. Less awesome would be using realistic (read: short enough to be controllable) flails, but they could still go for a reintroduction.
Crossbows - I still remember the hundreds of angry, angry threads about this before Oblivion was released. It's not terribly important to me, but I know a lot of people missed them.
Thrown Weapons - same category as Crossbows, more or less. I did use throwing stars occasionally for range, but they were never hugely important to me. More interesting to me was getting attacked by them.
Broadsword/Longsword - I guess you could also put sabers into this list. I can't imagine this being hugely important to anyone, but I'm sure there are people out there who prefer to fight with a bigger sword that isn't quite two-handed.
I put in an other just because I can't recall any others in the past, but they could be there. I never played Arena, after all. And if you would rather something new (whips, double-sided weapons, what have you) you can post that as well.