Dwarf Fortress 0.34.08 was just released. When a new (minor) version comes out, can I simply copy my save folder into the new install and keep playing with my original world and fortress, or would I risk some corruption/crash?
the developer has said that this version is compatible
As far as I can tell, old saves load up fine and have usable minecart/wheelbarrows, so feel free to move your data/save folder over to the new version.
Even though Toady has stated that the saves are compatible, always keep a backup. Recent updates are consistently unreliable. In general, the best way to see if a save is compatible is to simply try it. Keep in mind, various mods will prevent save compatibility. If you have a mod installed, make sure you install the most recent version of said mod onto the newest version.
One other thing. If you have a save you are concerned about, you may want to wait until a more stable version appears 2-3 weeks from now. There will be plenty of gamebreaking bugs in the first 2 weeks after a major release, and if you don't want to lose progress you should assume the worst.