Bleeding Birch - Bone-white tree that sprays a punch of foul-smelling red sap when you cut it down.

Dwarfwood - Trees made of petrified wood that must be mined instead of chopped. Dwarfwood can function as either stone OR wood in construction and crafting.

Meatspire - A "tree" composed of flesh and bone for evil biomes. Meatspire bone can be used as wood. The meat is edible. Its presence makes your dwarves uneasy for obvious reasons.

Giggleleaf - (not sure if this is possible) A rare talking tree for good biomes, which will interact with passersby as a legendary-grade comedian. Great place to build a tavern! It screams when cut down, which traumatises anyone nearby. Its wood is extremely valuable, though, especially if used to craft an instrument or toy!

Weepleaf - A tree that occasionally rains watery sap from its branches (behaves identical to salt water). Its wood is both fireproof and waterproof.

Woodwarden - A very durable tree that turns into a hostile treant if another tree is cut down within its vicinity. Turns into wood upon death, which can be used by carpenters to create especially sturdy armour.

Miner's Noose - A tough little tree that sprouts all over the place. Creates huge tangles of roots underground that are tough to mine through.

Yggdrasill Sapling - (This is 100% impossible to accomplish with current modding tools, but its fun to dream) A rare massive tree found only in the deepest forests. Woodworkers can be directed to carve stairs and rooms into it as though it were made of stone, allowing a fort to be constructed up amongst its wide branches.