Pretty much ANY amp can drive ANY speaker - at low volume. Matching is only essential when you plan to drive your system close to its limits. There are a number of factors to bear in mind.
Firstly speaker specifications will include how much power they can handle and what their impedance is. The power is quoted in Watts (W) and may be described as RMS (meaning Root Mean Squared) or PEAK. The peak output is typically twice that of the RMS but this will vary depending on many things inherent with the speaker design. The impedance of the speaker is simplistically a measure of the electical resistance offered by the speaker coils when current is driven through them.
Most cases of speaker damage are caused by using an amplifier that is under-powered. If you have, for example, speakers which can take 100W RMS and you are using a 20W amp, the "safe" region of your volume control is likely to be roughly one fifth of the way, assuming an even response to the volume knob. (20/100). The amplifier must provide the power to push the speaker coils in and out with the waveform signal for the music. If, at the peaks of the waveform the amp can't supply this power (because the volume is too high) then the waveform will "clip" with increasingly audible distortion. Clipping is harmful to speakers, and will usually damage the high frequency units (tweeters) first. Overdriving speakers with amps which are too powerful for them is also harmful. You must also consider what frequencies you are putting in the mix. Bass sounds have higher power demands than higher frequencies, so if you have the bass turned up high, your speakers are eating up more power at lower volumes.
Damage to amplifiers is usually caused by speakers which have too low an impedance. For example connecting 2ohm speakers to an amp which can't drive anything less than 8ohm speakers. Effectively, you are short circuiting the output stage of the amplifier.
In general terms, the safe thing to do is to buy amplifiers and speakes with similar power ratings, and make sure the power is at least twice as much as you are ever likely to use. In other words, the volume control knob should never go beyond the middle mark, and at that volume the sound should still be effortless, without distortion or other noises that indicate something in the system is working too hard. It is a bit like owning a car. You buy a car which has a large engine not because you will ever drive it at the top speeds it can theoretically do. But you buy it because when driving it at 80mph you still have heaps of reserves of power to use and the engine is not straining.