Affects Version/s: Minecraft 1.4.6, Minecraft 1.4.7, Minecraft 1.5, Minecraft 1.5.1, Minecraft 1.5.2, Minecraft 1.7.4, Minecraft 14w02c, Minecraft 14w03b, Minecraft 14w04a, Minecraft 14w04b, Minecraft 14w05a, Minecraft 14w05b
Fix Version/s: None
Here is how to reproduce since I can't explain this one very well either.
These steps go in correspondence with the screenshots.
1. Put a minecart onto a rail.
2. Spawn something. A skeleton is what I used. Push him into the minecart.
3. Usually, it will go off the rails by itself, since when the mob got in it pushes it in one direction. If it doesn't, make the cart go off the track.
4. Right-click to get in the minecart. You can get in it while the skeleton or whatever you spawned is still inside.
5. Either wait a few seconds or hit the mob to make it get out. It should now sink into the ground.