Mushrooms, dandelions, thistle, sticks, stones, and flint have stationary spawners that will respawn again after they are picked. Even if you build your house over a place where you picked one up, it will still spawn inside your house.

Bushes will respawn berries as long as you don't destroy the bushes.

Downed logs that are part of the landscape will respawn eventually.

Big rocks and ore nodes do not respawn.

Items that respawn mobs, like greydwarf nests and bone piles, will not come back when destroyed. Similarly, those boar runestones will not respawn boars.

For invisible spawners, some of them will cycle through appropriate mobs. If you kill off the boars, you might get necks there next time. And some of them spawn the same thing every time. Base items like workbenches and campfires will repress these spawns.

Most items inside dungeons do not respawn. The exceptions to this are yellow mushrooms, royal jelly and seekers in the mistlands.