From eHow "Shims are thin pieces of wood used to level cabinets, doors and other construction items that might otherwise vary due to elevation changes in the subfloor. . By placing shims below the lower-sitting cabinets, you can achieve a level height for all cabinets regardless of variations in the subfloor" Start at the low point and build up with shims to make level. The gap created at the bottom between the cabinet and the floor can be covered with either base shoe or scribe molding both of which can be found at your local home center or possibly supplied by your cabinet maker.

Read more : http://www.ehow.com/how_6595521_shim-kitchen-cabinets.html

Look on the bottom of your bookcase to see if they have screw-on 'feet' that can be adjusted so they sit level. I have a tile floor that isn't perfectly even too, and my husband had to adjust one the feet of the bookcases as it wasn't quite straight just the other day.

I'd start by fastening them all together. Depending on how much shimming they need, you could scribe the base of the cases so they match the floor.

Thank you both for your quick responses! The problem with shims is that I think they'd be visible especially since its white wood on light tile. These bookcases as you can see already come with a built in base molding so I think adding a second one to cover the shins would be a bit strange. Maybe the felt will work though if I only put them where there's a gap to the floor. Hopefully felt is subtle enough to not be super noticeable. They will be filled mostly with books and some board games/puzzles....

try mounting a cleat to the cabinet and then to the wall. After that screw the cabinets together and wa la your even!

Well, you would want to shim from the side -- e.g., on the right side of the right cabinet, to press it flush against the left -- so it wouldn't need to show. Alternatively, fill 'em up -- sometimes the weight alone will make everything settle a bit.

No feet just the wood base.

Fastening is a good idea. That'd make it very obvious when the unevenness is though they'd be a bit more difficult to maneuver as one long heavy piece versus four smaller lighter bookcases. I read up on scribing and see how it would work for wall shelves or the back of the bookcase but it seems like it'd be very difficult to scribe the base to the floor since its not just like a sloping wall but very subtle convex bulges across a dozen tile segments. Also I don't have the right tool or expertise to scribe them!

Acm that's a good point!