After purchasing 8 digital SLRs (major brand) for my place of work (their dime, not mine!) I put the cameras through their paces prior to sending them into the field. I had one which took tilted pictures. I thought I was going crazy, but took it to the dealer and after having 3 employees take very carefully composed images, checking edges, etc., we all came to the same conclusion- the sensor was positioned incorrectly during manufacturing. I would have other experience people try your camera, and you should try other cameras to conclude whether or not the problem lies with the camera.

Err, not wishing to be disrespectful, but this sounds more like pilot / user error than anything else. Switching on a grid will help in live view / viewfinder, but you say you do not wish to do that as a normal course of action. With the viewfinder or without a tripod it is sort of up to you.

I love the "taking off a shoe" suggestion, but that has terrain-based limitations amongst other things. :D

More seriously, I have also suffered from this symptom, and my remedy was to train myself to engage my brain prior to pushing the shutter button. Specifically asking myself whether the vertical / horizontal lines in the image were aligned in a manner that I wanted in the image. One can always correct after the fact, but not necessarily without compromising another part of the desired image.

The comments about movement in the process of taking the photo are also very constructive.

I hope that is helpful in the sense in which it is intended to be.

Good luck.

I've noticed that most all of my pics have a 10° tilt to them because I'm holding the camera lower on the right than the left. Is this a common thing, a characteristic of not holding the camera level in the first place, poor technique? What's a good way to overcome it? I'm thinking check for plumb or level against a vertical item in the frame. Maybe move the frame edge close to a vertical or level item to double check. It seems that I just have a natural tendency to frame things out of kilter. When I bring the camera up it seems like everything looks right in the viewfinder but the end result says otherwise. Don't want to have to always use live view with the level option in view. I have a D7000 and 18-200 DX. Your advise would be appreciated. Thanks.