I was just wondering, what are all the new weapons?

The player now has the ability to smith Dragonbone weapons, such as a sword, bow, warhammer, and so on. The new archery weapon introduced in Dawnguard is the crossbow, which comes with plenty of upgrades, as well as the ability to make a dwarven crossbow. I believe there are a few Dawnguard weapons that do extra damage to Vampires, but so far I've only seen a Dawnguard one-handed axe and warhammer. There is also another new weapon, but that weapon has something to do with the main questline, so I won't spoil you.

There are also new spells that can be used.

To expand upon the above post:

The new spells introduced are:

• Sun Fire - a bolt of sunlight that deals damage to the undead, and only the undead. (Restoration)
  
• Vampire's Bane - a ball of sunlight that explodes upon impact, dealing AoE damage to undead. (Restoration)
  
• Stendar's Aura - a holy aura that deals sun damage to the undead, similar to the destruction equivalent, ( Restoration)

There are also four kinds of bolts, coming in either Steel or Dwarven.

• standard bolt
  
• fire bolt
  
• ice bolt
  
• shock bolt

Other spells include

Restoration:
Heal Undead
Necromantic? Healing

Conjuration:
Summon Boneman
Summon Mistman
Summon Wrathman
Summon Avrek? (the horse)

The UESP has a full list of most of the new stuff. I was sad there weren't any nice looking clothing items though. ;-;