How to stabilize speakers without spikes.

After living with carpet over wood floors and spikes on my speakers for many years, my wife wants to have a wood floor (maybe tile) installed in our house

This will change the tonal balance of yr spkrs' response (usually upward). You'll get more mid-hi frequency reflections off the floor. This simply means that you probably have to change the spkr placement; you may get a more "airy", "detailed" (if slightly bass-light) sound -- and like it more.

As to the spikes you're using: you can continue using them by placing hard metal disks under the spikes (a nickel as suggested) -- but the result won't be exactly the same. Until now you've been coupling the spkrs to the floor mass... the metal disk will decouple them.

I strongly suggest you buy nothing and experiment with whatever you find at home -- or, in extremis -- just go to home depot & buy 3 vibration control puks.

Take one of your Vandersteen spikes to the local hardware store and purchase either hex or carriage bolts with the same thread size. They won't harm the floor and will provide solid contact and can be adjustable for desired tilt. This will cost less than $5. Another option is to find similar products from an audiophile web site and pay $100+ for similar, but much fancier, product.
The hardware store option worked great on my Meadowlark Shearwater HRs.

I recommend you try Soundcare Superspikes (http://www.soundcare.no) and they won't scratch your wooden floors.

Although my original post got lost in Audiogon never-never land, agree with Wellfed recommending Herbie's "Big Fat Black Dots".
Maybe there should be a contest to invent a more elegant name for these superb footers?
The impressive audible improvement is not critically dependent on the material beneath a "Dot".
Simply position a single floor tile under the front of each speaker raising the floor height just under the front of the speaker. Then the two front "Dots" go on top of this tile.
As far as floor material for an entire room, wood is traditionally better than tile when trying to reduce glare or listener fatigue. At least that's how it seems after listening to systems in many different environments.

Many years ago I owned the 'steens with sound anchor stands. I had wood floors and I simply put pennies with little felt dots on the bottom under the spikes. The whole operation probably cost about 10 cents.