Recommended Guitar Products

All links lead to an amazon.com page, but these (or something similar) can be purchased at most guitar shops.

Essentials - Products every guitarist should own

Snark clip-on tuner and metronome (red) - The best clip-on tuner on the market, and the least expensive.    
    Also comes in blue and black (no metronome)
Planet Waves String Cutter & Winder - The perfect tool for changing strings
Kyser Capo (for steel string acoustics & electrics) - Instantly and easily change keys
    or Dunlop Classical Guitar Capo (for classical/nylon-string guitars)
Microfiber Polish Cloth - Wipe down your instrument after playing to preserve it's shine and life span

Books

Mel Bay's Mastering the Guitar Class Method (Grade 9 & Higher) - Great book for class or individual use
Pumping Nylon - Great technical manual, complete with exercises for all guitar tricks
Aaron Shearer's Scale Patterns (Supplement 3) - A great book for practicing scales and sight reading.

Accessories

Music People FS7850B Guitar Foot Rest
On-Stage SM7211 Professional Folding Orchestral Music Stand, Black - A solid and relatively inexpensive orchestra-style music stand

Classical Guitars

I recommend Yamaha guitars for students; from my experience, they seem to be the most consistent in quality and playability. I wouldn't recommend buying a guitar online - be sure to go to a shop and find a guitar that feels right for your hands and your sound. Even guitars in the same make/model can vary.