Weapon skills (Archery, One-handed, Two-handed) : skill increases damage done. (0.5% per level. 50% increase at level 100)
Armor skills (Light Armor, Heavy Armor) : skill improves armor rating mildly (perks are where it's really at though). (0.5% per level. 50% increase at level 100)
Magic skills (Alteration, Conjuration, Destruction, Restoration, Illusion) : skill reduces magicka cost. Skill also unlocks new spells on spell vendors at 25, 50, 75 and 100. (about 41% reduction at level 100)
Lockpicking : skill broadens the target zone.
Pickpocketing : skill increases success chance to pickpocket
Speech : skill improves prices when buying and selling, and increases chance of success for persuade and intimidate.
Sneak : skill reduces detection radius for sight and sound.
Alchemy : skill improves magnitude of potion/poison effects.
Enchanting : skill improves magnitude of enchanting effects.
Smithing : skill improves armor rating of upgrading armor and weapon damage when upgrading. Does not improve item creation at a forge, only upgrading is affected by skill.
Block : skill increases percent of damage blocked.