A list of all the characters that can, in my opinion, effectively jungle at the moment
Standard items: Cloth Armor + 5x potions
Best Jungling Runes:
I use Armor, Attack Speed, HP for jungling.
The glyphs are dependant on the champion, but are somewhat useless.
Masteries:
The standard jungling masteries are 1-16-13 or 1-18-11, going for Mana Regen, HP, Smite, Ghost, Armor, and the XP masteries.
I however, tend to use 1-13-15 (Movement speed) for faster jungling, on characters like Rammus that do without the defensive masteries.
Amumu
RUNES: Armor, hp, MPEN
Starting Items: Standard
Summoner Spells: Ghost and Smite
Akali
RUNES: Flat AD, flat AP, armor, hp
Starting Items: Dorans Blade, Longsword, Standard
Corki
RUNES: Attack speed, armor (Probably)
Starting Items: ???
Chogath
RUNES: I have no idea
Starting Items: ???
Blitzcrank
RUNES: Cooldown Reduction, Flat mana, hp, armor
Starting Items: EoF + pots (Yohacchins proposal)
Mundo
RUNES: HP, armor, HP regen, armor pen
Starting Items: Standard (Maybe. Testing soon)
Evelyn (AD)
RUNES: Some flat mana, Attack speed, HP, armor
Starting Items: Standard, Mana Crystal + 2x hp pots
Fiddlesticks
RUNES: Standard caster
Starting Items: Standard, Elixir of Brilliance + potions, pretty much everything with AP
Gragas
RUNES: HP, armor, armor pen, attack speed
Starting Items: Standard, ???
Heimerdinger
RUNES: AP, or almost anything
Starting Items: Standard, EoB
Irelia
RUNES: Attack Speed, armor
Starting Items: Standard, ???
Jax
RUNES:Attack Speed, Armor Pen, HP, Dodge, Armor
Starting Items: Standard
Karthus
RUNES: Mpen, Armor, HP, CDR, etc
Starting Items: ???
Malphite
RUNES: Armor, HP
Starting Items. Standard
Master Yi
RUNES: Attack Speed, hp, armor
Starting Items: Standard, EoA + potions
Mordekaiser
RUNES: ???
Starting Items: ???
Nasus
RUNES: Attack Speed, HP, Armor
Items: Standard, EoF
Nunu
RUNES: HP, Armor
Items: Standard, probably EoB too
Olaf
RUNES: Attack speed, armor pen, armor, hp
Items: Standard, EoA, EoF
Poppy
RUNES: Attack speed, armor pen, armor and HP will do
Items: Standard
Rammus
RUNES: Armor, armor, armor + armor
Shaco
RUNES: No requirements
Items: Standard, EoB
Shen
RUNES: Armor, HP
Sion (AD)
RUNES: Attack Speed, armor pen, armor, hp, flat mana
Items: Vampiric Scepter, Standard
Trundle
RUNES: Attack Speed, Armor Penetration
Items: Standard or Vampiric Scepter
Tryndamere
RUNES: Armor Penetration, Attack Speed, Crit DMG?
Items: Vampiric Scepter, EoA, Standard
Udyr
RUNES:Flat Mana, Attack Speed, Armor
Items: Standard, Mana Crystal
Vladimir
RUNES: HP, HP Regen, AP
Items: ???
Warwick
RUNES: Attack Speed, Armor
Items: Standard
Xin Zhao
RUNES: Attack Speed, Armor
Items: EoA, EoF, Standard
For invidual jungling guides you can ask me. These are, in my opinion, the current characters that are intelligent to jungle with. Some are better, some worse. I'm pretty sure EVERY character could go in the jungle, but not as effectively.