The version I am using now is the AM transmitter based on the 555 IC chip schematic in photo 3 with build instructions here:
I built this transmitter and placed it in a plastic container. ANT is about a meter of wire coiled up in the bottom of the container.
This transmitter works very well and transmits the signal all over the AM band. Just place the radio near the container, turn on transmitter and you are good to go. You get a very nice strong "beep beep" sound (sidetone) with this version. Number of components is still very low but you have to do some wiring and soldering. I built this one on a breadboard and then just transferred it to a circuit board and soldered the jumper wires. Not very elegant perhaps but I like the spaghetti wire look.
There is some question as to type of capacitors to use: I used simple round ceramic disk caps but the original link picture shows them using polarized caps so I think either works. Perhaps one works better than the other, will have to try an experiment on that. Probably C1 should be polarized, C2 ceramic disk.
Version 2: (photos 4 and 5) using 1 mhz oscillator crystal
This was my original transmitter based on schematic in photo 5 and this instructable:
I had built this transmitter first and it is definitely the easiest with only a couple of components. It is also the most powerful transmitter but who needs power for just practicing keying? The thing I did not like about this one is that it only transmits a carrier wave with no modulation (no sound) so you only get a "buzz buzz" or "shh shh" sound by turning the carrier wave on and off - not very pleasing.
Note: I also did a version 3 which was to combine versions 1 and 2 with an audio transformer to modulate the sound output from the 555 chip into the 1 mhz oscillator. It did broadcast a strong carrier and audio signal but the downside is that there was a terrible pop sound when I let up on the telegraph the key. That could be fixed with an RFI choke but was too much work as I just needed to transmit a clean signal to the AM radio which version 1 performs nicely.
I have learned how to send Morse Code pretty well now but listening at speed is still a challenge but am slowly getting there.
Photo 6: Picture of my 1/4 watt 40 meter Michigan Mighty Mite ham radio that I cannot legally use until I get a license. Just wanted to make one.
Photo 7: Picture of my portable practice CW keyer. See my instructable for details.
Update 1/18/201: I am learning more and more about radios as I go along. I found out that in "real" ham radios the transmitter doesn't send a sidetone, rather it is gotten from the transmitting oscilliator carrier by the receiver - called Beat Frequency Oscillator - so you have to have a special short wave radio receiver that has the capability of demodulating the signal from the carrier wave - usually. I just built a QRP Michigan Mighty Mite transmitter, which I cannot use because I don't have a ham license - something I hope to do one day as you just have to pass a 35 question test for the entry level Technical License. But I am building a cw receiver for the 40 meter band so that I can get practice at listening to live cw code. It is very interesting learning the concepts that allow you to understand what is going inside the little "black box" radio. Learning about inductor coils and resistors and capacitors and transistors and how they function is fascinating.
Update 2/18/2013: I built the Michigan Mighty Mite Transmitter shown in the last picture. This is a real HAM transmitter that is not legal to use without a license. I hooked the antenna leads to a 50ohm resistor so that it wouldn' t transmit farther than my room and was able to hear the signal on my shortwave radio that allows me to hear CW or Morse Code. The receiver demodulates the signal from the transmitter carrier. You can find lots of details on how to build the MMM on the internet.
Update 4/13/2013: I have since built a couple more little transmitters and put them in tea tin boxes, built rf detector (fun to see what is producing rf signals and if my rc transmitters are working, wattmeter probe, a Ramsey HR-40 reciever (fun to experiment with but not the greatest receiver, and bought and use a Tecsun PL-660 SW receiver for listening to CW - fantastic little radio. Also built an antenna tuner which greatly increases receptivity. Have learned Morse Code but listening is a skill that is going to take a while. Practicing at 5/20 words per minute. No end to the stuff you can build and it is fascinating. Need to get a ham license but have to wait a year to get back to States.
Update Aug/2013: added photo of a bamboo key I bought. Pretty.