Align all the cabinets so they all flush, plumb and level with one another with shims, then, find your studs and screw into the studs through the back of the cabinet. I would do two screws at the top, two in the middle and two on the bottom of each cabinet.

If you get lucky there is blocking in the wall between the studs for the cabinets to attach to.

Do NOT use drywall screws (even long ones).

You may need a stud finder to locate blocking and studs.

This post was edited by brickeyee on Thu, Nov 29, 12 at 15:43

Thanks guys! But... I think my question is yet to be answered.

See, finding studs and blocking is not a problem. But after all the alignment and leveling effort, when there is a gap between the cabinet and the wall, do you just screw right through the back into the wall? Wouldn't the screw try to close the gap? If so, wouldn't it try to pull the cabinet out of alignment?

Or, am I worrying too much?

You've got your top two screws shimmed and then drive them home. The middle and bottom screws you drive till they are just snug and then stop. These screws don't really hold much if anything and should not be driven home. Use cabinet screws with the built in washer.

ahh... got it. All makes sense now. Thanks!!!

Screws go through each shim and and those screws are tight.
The screws at the contact point without shims are snug but not tight.

Other screws (especially with a gap to the wall) are simply snug to the surface.

If the cabinet will hold significant weight, then every screw with a gap should be shimmed and pulled tight.

The 'washer head' screw style is better (try McFeeley's).

This post was edited by brickeyee on Sun, Dec 2, 12 at 10:52

The way to get "full shim effect" at all points would be to carefully mark the size of the top and bottom shims, remove the cabinet, tack the shims to the wall at their proper positions, and use a straightedge to determine the needed shim thickness at the in-between points based on those predetermined perimeter points. That way you are actually identifying co-planar points that guarantee a flat true cabinet back.
You don't hear this mentioned frequently, but in addition to being plumb and level, the adjoining fronts of cabinet runs must define a true straight face line. This can require prodigious amounts of shimming.
Casey

Shim the largest gaps, screw through them,ten install the shims in the smaller gas with nothing but hand pressure to push them in (no hammering) and then screw them through the cabinet.

Make sure you use two shims at each spot to get maximum bearing area.
Tapers in opposite directions.

This post was edited by brickeyee on Sun, Dec 2, 12 at 10:55

Another option is to use a French cleat. This is a board you attach to the wall that has a beveled top edge, you screw a mating board to the back of the cabinet with the bevel on the bottom to that you can hang the cabinets from the cleat. You level and shim the cleat on the wall (much easier than doing it with heavy cabinets!) then hang up your cabinets, slide them left and right as needed and then add screws to hold them in place. For a problematic wall it can be much faster than the usual methods, its a whole lot easier when you're working solo.

Thanks all for the input. Thankfully, we only have two tall cabinets connected together that I'm most concerned about. We ended up pulling them out, and shim the wall where it bows in. Recorded the locations of the shims and pushed the run back as one unit. It's nice to be able to push and already have everything plumb. Then we screwed through the back and shim at the pre-recorded locations.

The French cleat sounds pretty cool, but I wonder if it automatically pushes the cabinets out across the run. Kinda have to plan for that if it does.

There are metal versions of the 'French cleat' that have almost no additional thickness.

they attach to the cabinets box on each side, and then bend in snug against the back of the cabinet.