What are your tricks for grinding skill levels? I'm especially interested in Speech, but I have a good one for smithing.

Dwemer Arrows. Firewood is free, you can load up on Dwemer metal very easily for free, and the arrows are quite valuable.

Pickpocketing coins back from skill trainers.

Knowing certain Bosmer in Riften who works at the Blackbriar Meadery has many benefits for a character with an Iron Tongue
Conjuration, cleanse the Fonts at the COW for almost unlimited Magicka and Magicka Regen, cast Soul Trap at a Skeleton or Dead Draugr in the Midden.
Alteration,...,cast Detect Life in the COW courtyard, use Telekenesis to play hoops with a Skull and the basket in the players room at the College.
Illusion,..., cast Muffle, rinse, repeat.
Restoration,..., cast Turn Undead at the Draugr in the Midden, there are also a few Skeletons that reanimate when the PC is near.
Armor Skills and Block, Mudcrabs are friendly when offering Skill Training. A skeever/wolf pack can be forced into constantly attacking the PC if the PC has thier back to a rock wall or large boulder.