I've been giving a lot of thought lately to what the smallest practical size for a telescope can be. The Rev. TW Webb, in his seminal work "Celestial Objects for Common Telescopes”, made mention of a rather small telescope with a tiny aperture that he used for very basic observing. It must also be remembered that Galileo's first telescopes were very small (as was the one used by Giovanni Battista Hodierna for his deep sky observing). While many amateurs shirk at the idea of anything smaller than a 4"/100mm being used for serious observing, it should be remember that many beginners do not have the sort of money that sort of instrument almost always costs.
If a beginner has graduated from binoculars but still lacks the funds to purchase a larger instrument, a typical 60mm would probably suffice. However, I am curious to see what can be done with even smaller instruments. The first telescope I did any serious observing with was a Tasco 50mm, and was able to make out many of the brighter Messier objects. What I am curious to see, though, is what can be seen with a 35mm or 40mm instrument.
40mm telescopes are actually out there. Meade sold a nice one that was available through Wal-Mart for a while. Let me qualify that; the main objective was nice, the rest was somewhat questionable; the diagonal in mine had a second surface mirror, the eyepieces were cheap .965" units, the interior of the OTA was left in bare aluminum and the tripod was a little tabletop unit that was basically useless. However, most amateur astronomers have the parts to overcome these, if not the skill.
What you can expect to see with a small telescope in this range would not be too different from the view afforded one through binoculars. There are numerous books out there dedicated to binocular stargazing that can readily cater to the small telescope user. Under good observing conditions (magnitude 5.5), a 40mm at a modest 20 power can see down to magnitude 10.5, well within the range of many deep sky objects. While resolution might not be great, for basic, lightweight stargazing, it is perfectly suitable.
At this time, I've limited most of my work with my Meade 40mm (named "Vic") to studies into Galileo's and Hodierna's observations. However, I think I might just try some actual observing with this tiny instrument.