Replace Stone Bricks and Cobblestone with Mossy or Cracked Stone Bricks and Mossy Cobblestone. The closer you get to the water, the more mossy blocks there should be.


You can also replace Stone Bricks with Cracked Stone Bricks, especially near craters from explosions.


Use Slabs or Stairs from any material to make holes in a wall. This looks really cool with Stone Brick walls, because it looks like there's a brick missing.


In a wall of Fences, make 1-block holes scattered around, and replace some of the Fences with opened Fence Gates.


Make stone paths and walls look old and weathered by scattering Cobblestone, Gravel, Cracked Stone Bricks, and other types of stone around - check out Patriots_Terran's fantastic tutorial on roads for more! They also have a wall tutorial worth checking out.


Board up doors and windows with blank Signs.

Break Glass Blocks and Panes, and replace some of them with Brown Stained Glass to make them look like they're covered with dirt.


Scatter furniture around the insides of houses, and get rid of some too. (Getting rid of furniture could imply that someone went in and stole it. Anything for a nice armchair, I guess...)

To add "graffiti", cover one or two walls with paintings, especially if your building's in a city. But it works in other places, too, as long as someone's got access to a blank wall and some spray cans :D


Break or turn off any Redstone Lamps, or leave some on if you need to.

If your building was inhabited by people at one point, or if someone was killed there, you could put a Skeleton Skull somewhere. Redstone Dust makes nice "blood".

Fill Chests with Cobwebs and String, and other objects the building's residents might have left behind.

Put empty bottles in Brewing Stands.

Replace blocks with darker blocks of the same color to make them look dirty or wet, and lighter blocks to make them look faded. This can be used to make stains on tile floors, rot on wooden floors, and other things.

Hardened Clay looks kiiiiiiinda like rust on Iron Blocks, but I wouldn't use it too much, because there's a pretty big contrast between the two blocks.

Wood plank types in order of darkness:
Birch -> Oak -> Jungle -> Spruce -> Dark Oak


Make some blocks subject to "gravity", that is, break them and place them onto the floor directly below them. This is useful for caved-in roofs (rooves? XD).

Use SethBling's SetBiome filter for MCEdit to change the biome to Desert, so that grass, leaves, and other plants look dried-up.

Replace Oak/Acacia/Dark Oak Leaves with Birch Leaves to make them look a little withered.

Replace Saplings and Ferns with Dead Bushes.

Put Cobwebs in corners, and if you really want to, hide a Spider spawner somewhere, or spawn some yourself. (If you name them, they won't despawn unless you switch to Peaceful!)

Making overgrowth:
- Add patches of Grass and Dirt "leaking in" from outside, especially near windows, doors, and other open places.
- Add Vines growing along the walls, and use String to control their growth if needed.
- Use Bonemeal. A lot.

If there's any place where rain can fall to the floor, add a little bit of overgrowth there, and make any wood there look "rotten". 

(This pic doesn't have all of the details from above, it's just there to show plants growing under a hole in the roof :P)