For me, I'd love to see the following:
Sarissa Pike and Tower Shield, as well as a companion combat technique like shield wall, and the ability to thrust while blocking instead of merely bashing.
Halbards
Hand-and-a-half swords
Flails
Spears
Atl'atls (c'mon, Mammoth without an Atl'atl?)
Throwing Knives
Note on the Sarissa Pike/Tower Shield. at an 18 foot melee advantage, the sarissa pike should decrease run speed by 25%. Further, the tower shield should disable running and make you have to march, dropping you to 90% speed when you raise to block. Instead of bashing with the tower shield, you should merely thrust with the spear/pike/sword, or make a 70% smash with a mace/axe.
Spears should thrust and leave bleeding damage. When used with poisons, the bleeding damage should be doubled (same goes for axes with perks in my opinion).
Flails should merely mimic maces.
Halbards should thrust and cut, similar to a spear/axe hybrid (as it is).
Why don't companions have a tactics wheel? I would love if I could set my companion to stay in a spot and stealth shot with his bow while I engage the enemy, or lock shields with me as we advance on the enemy. Bah!
Armor - Get rid of Light/Heavy trees, and make a single Armor tree with similar perks to the Light armor tree, then add a new tree for pikes/spears/thrown weapons instead.
Change Smithing so you can smith anything, but your smithing level effects the outcome (weight diminishes and armor value increases as smithing level increases), and Set bonuses are applied when/if you choose set perks (Elven now makes you better at X,Y,Z). Allow certain sets to hit the armor cap while other sets fall short but add to offence more. class sets as light/medium/heavy merely as a formality to show which has the best defense(Heavy), or offense(Light), or is set at a middle-road deal (medium). Not allowing each set to hit cap and giving them each unique bonuses from the smithing tree allows for more meaningful selection at endgame in terms of style of armor (I prefer Steel Plate to Daedric in my opinion)
These are just flights of fancy, of course, I love skyrim as it is, but wouldn't this just add so much more?

Any other ideas on how the weapon/armor choice could be built upon? Not just a weapon to see, but actual implementation would be nice
