You may want to search www.johnbridge.com forums. This is mostly a tile site but they've covered pretty much every flooring scenario there is.

I would think you'd try to avoid having to remove the adhesive because that's not going to be easy. But the engineered flooring is so thin that it may not sit right over the hard glue. Typically engineered flooring can float or be adhered so it's not absolutely necessary to glue it down.

Hmmm...what about laying your floor down right on top of the existing one? Remove the baseboards, put down a thin layer of sound proof material and lay the floor right on top of that. You'll have to adjust your transitions to your doorways because the floor will be slightly higher. Just throwing out ideas. Removing tiles glued to concrete does not equal fun.

...then either repaint old baseboards or put up some nice fresh baseboards to match your new floor.

I guess if the tiles are already loose, that may be an issue with laying a floor over the top. Are most of them loose or just a few?

Here's something on floating floors:

Why use the Floating installation method?

"Expansion and contraction (movement) within any wood flooring takes place when prolonged relative humidity changes occur within the homes environment. Engineered wood flooring is overall more stable than solid wood flooring and separations between boards during the relative humidity changes are less with any engineered flooring which adds to their appeal to use in basements or in tropical regions of the country where higher moisture levels are common. The benefits of using Floating wood floors is that the floor boards are connected to themselves, not the sub floor making the whole floor move independently as one "Unit", thus the seams between the floorboards will not open up and any movement is only shown around the edges of the room which is hidden by the baseboard or 3/4 round molding on top. With wood flooring that is direct glued or stapled down to the subfloor the floor boards will act independently from each other and possibly show gaps between the boards if the relative humidity is low for a prolonged period of time.

Most engineered flooring brands can also be direct glued-down over a concrete slab above or below grade, or stapled down over a wood subfloor. Floating wood floors can be installed on any grade level. Most manufacturers allow their floating floors to be installation over other flooring such a tile, vinyl and radiant heat." quote from: http://www.hoskinghardwood.com/floating-wood-floors.asp

We have similar floors (oak parquet on concrete) and our contractor told us we'd need to lay down plywood first, and then affix the new wood floors to the plywood. This gets you the added hassle of putting down two floors, but maybe out of the hassle of getting the glue up? Good luck!

I guess I'm afraid of doing my own demolition. You never know what your going to pull up (lead asbestos who knows). My suggestion is that you replace the loose parquet tiles with new unfinished oak parquet - sand and strip the entire floor - then stain a beautiful chocolate or ebony. it seems easier to rent a floor sander than a jackhammer. Check out some of the stained parquet floors in Kelly Hoppen's Kelly Hoppen Style.

One more thing on adhesive removal--you may be able to lift up the tiles and scuff the adhesive smooth rather than removing it. The idea would be to create a surface similar to a brushed concrete.

Thanks you all, esp Art.
I'm bucking the dark floor trend and installing white maple.

I've gotten every type of advice including : install a plywood subfloor then glue (or nail) down, don't bother with the plywood (just glue right onto the old adhesive), cover the old adhesive with Ardex self leveller (dries in hours) then glue down.
I'm guessing that I'll end up removing all the tiles and then evaluating whether it will be better to install a plywood subfloor (and not bother removing the old adhesive) or to remove the old adhesive and lay down new adhesive, or lastly to just leave the old adhesive in place and add new bostick best on top of it.
Please keep your comments coming.