Have you tried Blu-Tac or White-Tac? It is a silly putty type product that you would roll into small balls and place between the speaker and the platform.
If you don't want to use blu tack, you can use cabinet door bumpers. The clear ones, they are about 1/8" and have adhesive that you can apply to the stand. When it comes time to remove them, they just pop off without leaving damage. I prefer these to blu tack because they provide a flat surface for the speakers to sit on, and they are cleaner when you remove them.
First of all, are your speakers moving because they're not level?
If they are level, and you can bolt them down, here's what I'm doing with mine. I have them spiked to the stand using Audiopoints and their corresponding discs. It tightens up everthing a lot. I then went out and bought longer bolts, and just barely seated them. This way if they are going to move, it's not going to be very much, and they won't come off of the stand.
Grip It shelf liner would work great for this. This is a link to an E-Bay auction so you have an idea of what it is, but you can find it at many grocery stores, Target, Walmart, etc., and it comes in several colors. It just lies on the flat surface without adhesive, and it's rubberized so it prevents slipping.
If you don't mind working to remove the Blu-tack from the bottom of your speakers and the top of the stands when you decide you want to re-arrange things, then I agree with the Blu-tack or Quake Hold (museum wax) method. If you want something that will keep the speakers from slipping, but is less permanent and will not leave behind any residue, then try the Grip It shelf liner.
My favorite tweak for securing monitors to stands is artist's kneaded eraser. They come in small gray butter pad size squares and can be shaped or compressed into any shape. Kinda like Silly Puddy.
They do a great job of locking your monitors to the metal stands. I've accidentally bumped my speakers sitting on stands with 20 pounds of steel shot in them and had the entire structure lurch without the speakers coming unstuck.
Kneaded erasers have a fine light powder in it which prevents it from permanently adhering to the wood veneer on your speakers. I've had monitors on stands for three years that came off without leaving a trace. It never gets sticky or gooey, and never discolors the wood. Remarkable stuff.
My favorite material is Sorbothane. Audioquest sells (or use to anyway) it in sheets with adhesive on one side. It can be cut to form pads that you can rest the speaker on. The adhesive is unnecessary for this application, but it never seems to cause a problem. Stick the adhesive side to your stand. The Sorbothane will stick to your speaker bottom when you place the speaker on it, but it can be removed without damage. I have never had any speaker finish damage using this method. If you let your speakers sit on the stands, after a while they will be stuck as if glued (more like suction though). No need to worry, just apply moderate pressure on top of the speaker - attempting to tilt it while holding the stands steady (I usually stand on the base of the stand). Use your body or arms to prevent the speaker from falling if it realeases suddenly - this is just a precaution, when moderate steady pressure is applied, the speaker releases slowly. Be patient, and the Sorbothane will release after several seconds of steady pressure. The Sorbothane may end up on the speaker or the stand, but it is easily peeled off if you go slowly.
I have found that Sorbothane is better than any other method including spikes and blu-tack. It connects the speaker to the stand very solidly and has never caused any damage to a speaker I have used it with.