A balance bike is a small pedal-less bike used for teaching toddlers how to ride, and they offer many advantages over using training wheels. If you'd like to read more about balance bikes, twowheelingtots.com is a great site with loads of information.
There are many commercial balance bikes available, but they can cost quite a bit. I made this balance bike from a used child's bike in a few hours, and it only cost me $5.
There's slightly more to it than just removing the pedals, crank, and chain from an old bike and just plunking your kid onto it . . . but not much.
Take a look at how I tackled this project, and let me know what you think. Hopefully there's enough information here to help you make your own. Thanks for looking!
Step 1: Find the right candidate
To achieve this as easily as possible, I recommend looking for a bike with 12" tires, and a frame that is designed with one main tube that goes from the head tube to the seat post/bottom bracket area. A lot of kids' bikes have frames shaped like this, so it shouldn't be too hard to find. Bikes with this kind of frame should be pretty easy to modify to get the seat just a little bit lower than what is possible as they come from the store. (I would specifically avoid traditional-looking frames if you can, as they will require a lot more work--welding and such--which is beyond the scope of what I was willing to do for this project.)
I found this one at a thrift store, and it happened to already have two decent tires and inner tubes that didn't need patching. Nice find!
After some very slight modifying of the seat tube, the seat is low enough for my 2-year-old. The nice things is that the seat is still adjustable so I could raise it up if we needed to in the future.