I really like BEAM bots ( http://www.beam-wiki.org/wiki/Main_Page ) because the electronic circuits are relatively simple so you can focus on the looks of your bot.One of my favourite types is the Magbot pendulum.A stationary bot which works not unlike a electromotor.
What you need to make one is this:
-solarcell
-3300 uF capacitor
-1000 uF capacitor
-2n3904 or 2n2222 transistor
-2n3906 transistor
-diode
-2 x 100K resistor
-LED (not necessary but it uses otherwise wasted energy so why not.....)
-coil. You can buy these at Solarbotics , http://www.solarbotics.com .Or salvage one from a videorecorder.
-magnet (neodymium magnets are great for this)

This is for the electronic circuit,what you use for the stand is up to.Make it big,make it small,make it short or make it tall(yes,I'm a poet ;) )At this time I wasn't sure what I was going to use for a stand yet but I did know I wanted to use a wooden ball as the pendulum bob(the part on the end of a pendulum).

Step 1: The Electronics

First let's solder most of the electronic circuit together.The easiest way is to start with the two capacitors.Solder both negative leads together.Then take the diode and solder the positive lead to the positive lead of the 3300 uF capacitor.The negative lead (where the stripe is)goes to the positive lead of the 1000 uF capacitor.
Take the 2n3904 and 2n3906 transistor (hold the flat side towards you).Solder the right lead of the 3904 to the middle lead of the 3906.
Get the two 100 K resistors and solder them together.Solder the right lead of the 3906 transistor to one end of the resistors.
Solder the middle lead of the 3904 transistor to the the middle of the two resistors.
Now lets join the two parts of the circuit together.The left lead of the 3906 transistor goes the positive side of the diode.The left lead of the 3904 transistor goes to the negative lead of one of the capacitors.

At this time I usually put the electronic circuit to the side and start working on the base(it is easier to solder the LED,coil and solar cell on later when you decide where to place them on the stand)

Many thanks to Solarbotics(http://www.solarbotics.com )for letting me use the image of the circuit.

Step 2: Make a Stand

For the sake of simplicity(and to make it easier for people to make one of their own) I chose to use a box made out of wood for the stand.
I used left over wood which meant it was very thick (22 mm).The box measures 140 mm x 95 mm with a height of 120 mm.
Of course you also need something to hang the magnet from.For this I used a piece of 12 mm dowel,250 mm long(I got mine from American Science and Surplus http://www.sciplus.com/ )On this I attached a brass t fitting,then a 65 mm long piece of dowel was attached to that.
I took a brass end cap,drilled a hole in the side and soldered a piece of copper wire on it.The wire was then bent into a hook.
The cap with hook went onto the end of the short piece of dowel.
In the lid of the box I drilled a 12 mm hole for the dowel and a shallow 22 mm hole for the coil.I also drilled two holes for the wires of the coil.
After deciding where I wanted to have my solarcell and LED I drilled holes for those.It is a good idea to have the solarcell on one side and the LED on the other,shady,side.

Now it's time to finish up the electronics.......

Step 3: Electronics Part II

Solder two leads to the LED (mine was salvaged and already had some).The positive lead goes to one of the negative leads of the capacitors(yes,this is correct).The negative lead is soldered on the right lead of the 3906 transistor.For the coil solder one piece of wire to the negative side of the circuit(one of capacitors negative leads)and another one to the right lead of the 3906 transistor.
For the solar cell solder one wire the positive side of the 3300 uF capacitor and another one to the negative side.

Get the wooden box,put the electronic circuit inside,then push the two solar cell wires through the holes for them,solder the solar cell onto these.Do the same for the coil,the outside wire of the coil is connected to the negative side of the circuit.The inside wire is connected to the right lead of the 3906 transistor.Push the LED through the hole you made for it.
I put a brass piece around the LED.

Now is a good time to test if the circuit actually works once you put it together.
If it does it's time to finish it all up......

Step 4: Putting It All Together.

Screw the lid on the box,remember to use non-magnetic screws for this.In my case I used three(because that's all I had)salvaged brass screws.
Glue the dowel assembly onto the lid,you might need to give it some,gentle,persuasion with a hammer.I glued a wooden knob on top of the dowel assembly.
I gave my stand a varnish of boiled linseed oil.If you decide to do that as well,now is the time to do so.
Glue the coil in place,I used a little brass part I had,in the center ,to finish it all off,Glue the solar cell on the box.
Get the wooden ball and drill a hole in the bottom the same diameter as your magnets (in my case this was 10 mm ).A drill press is highly recommended for this.Then drill a hole for the hook on the other side.I used the same kind of copper wire as I used earlier for this.
Glue the magnets in place and the hook.
Get a piece of string and hang the ball from the hook on the dowel.Keep the distance between coil and magnet as short as possible.