Description: Does it bother you that you have a disembodied hand in first person? What about the fact that you can only see a very small portion of your skin then?
This mod makes your third-person player model show in first person, so no more disembodied hands. :)
Those aren't the only reasons you might want this mod, though. Having this mod makes you feel like a boss while you're running. Being able to see two hands moving like you're actually running really is cool.
Also, bows are held in your left hand (like real-life right-handed archers), which also feels quite epic.

Links: Forum link

Notes: This mod is a coremod, and it also requires the RenderPlayer API and Kes5219's utils mod (link in the files page for the download).

Installation instructions:

Install Minecraft Forge.
Place the .jar inside the file you downloaded for Improved First Person in .minecraft/coremods/.
Place the .jar inside Kes5219's utils in the same folder.
Install the RenderPlayer API by putting the contents of its zip inside minecraft.jar (you should read its installation instructions to be sure, though).

Improved First Person