Troubleshooting electrochemical batteries For my science classes, I have built multiple types of electrochemical batteries utilizing oxidation-reduction reactions, and I have demonstrated that they each produce potential difference across the different solid metals used using a voltmeter.  Unfortunately, I have been unable to harness any of this to light up a simple lightbulb.

For my first demonstration, I used a copper and zinc strip in vinegar solution.  There was a voltage difference across them of about 0.9V.  This was lower than the 1.1V I was expecting, so I hooked up two of these in series to produce 1.8V.  I attempted to light a simple light bulb (which works perfectly with a 1.5V D battery), but there was nothing.  No current flowed.

For my second demonstration, I made a voltaic pile with cardboard in vinegar, zinc discs, and copper discs.  Again, I had a great voltage prepared (about 3V or so), but I could get no current.

For my latest demonstration, I tried a 1.0M CuSO4 solution with a Cu strip in it connected to a 1.0M ZnSO4 solution with a Zn strip in it via a salt bridge of 0.2M KNO3.  The voltage difference was about 1.1V spot-on, but again, I could get no current to flow through the light bulb.

What could I be doing wrong?  Is there something fundamental I am forgetting here, or is there something perhaps wrong with the items I am using?  My original copper and zinc strips were about 1mm thick, if even that, so I replaced them with thicker strips in later demonstrations, but that did not fix anything.
Your experimental procedures seem to be perfect. There is just one minor error in your conclusion: you said that no current flowed. I disagree - current flowed, just not as much as you hoped. Harnessing one of these reactions to light up even the teeniest lightbulb would be similar to harnessing a bumblebee to a model airplane.

Getting a visible change upon connecting the battery is a reasonable goal. In one sense, you have already done it, by observing the needle move in the voltmeter. I know, you would like something more. A mechanical device might work well: say, a compass needle next to a coil of wire. When you connect the battery, some current will flow, some magnetic field will be generated, and the needle will move. 

Another possibility: if you take a small battery operated clock (either mechanical/quartz or digital) and remove the battery, you should be able to operate it with one of your batteries (you may have to boost the voltage). These devices use very small amounts of current, in the range that your batteries can provide.