Small is a relative word on this shelf, and it usually means under about 100mm. The useful question is not whether a small telescope is worth having but what it will show, and the answer is a great deal more than most people expect.
What every small telescope shows
Lunar craters in detail, the phases of Venus, the four bright moons of Jupiter and its two main cloud bands, Saturn's rings as a clearly separated ellipse, double stars, and the brightest clusters and nebulae. That list contains almost every sight that makes people fall for astronomy in the first place.
Where it stops
Faint galaxies, most nebulae from a light polluted sky, fine planetary detail, and resolving globular clusters into stars. Those need aperture, and there is no accessory, eyepiece or filter that substitutes for it. Knowing this in advance is the difference between a satisfying small telescope and a disappointing one.
Why small instruments get used more
They cool quickly, set up in a minute, weigh little and can be left by the door. Over a year of ordinary weather, an instrument you take out on a whim will show you more than a larger one that needs a decision. That is not a consolation prize, it is the main practical argument for buying small.
Mini, compact and what the words hide
Mini and compact are marketing words rather than specifications. The only figure that tells you what an instrument will do is the aperture, which is why this index publishes it beside every price and refuses to publish a price without it.
Questions people ask about telescope
What can you see with a small telescope?
The moon in detail, the phases of Venus, Jupiter's moons and cloud bands, Saturn's rings, double stars and the brighter clusters and nebulae.
Is a small telescope worth buying?
Yes, particularly if it means observing more often. It shows almost every sight that makes people take up the hobby.
What counts as a small telescope?
Broadly anything under about 100mm of aperture. Below that the instrument is still real; the limits are on faint objects rather than bright ones.