The first type of amps that came along had to be the tube amplifiers. Funny thing is, even though the technology of tube amps is fairly old, these amps are still used widely among pro and beginner guitar players. The reason for their popularity is that the tone of these amps is usually very warm and natural compared to the other types. Not only do they sound better, they are usually louder than amps of other types and the same power level. The only thing to remember with tube amps is that they require maintenance because the vacuum tubes need to be periodically changed.

Usually there are two types of tubes in an amp - the preamp section and the power section. Common tubes are 12AX7, 6L6, EL34, and many more.

There are many different brands of guitar amps that use tubes -- Marshall, Soldano, Peavey, Genz-Benz, Mesa Boogie and many others -- especially older and vintage guitar amps.

Solid state amps were invented to replace tube amps (which didn't happen!). Basically, the main difference between tube and solid state amps is that solid state uses transistors instead of tubes. They also require almost no maintenance because there are no tubes to change.

This is not to say that solid state amps are not as good as tube, it just all depends on the application and type of music you are going to be playing.

Some guitarists prefer colliding the two and making what is called a hybrid amp. This type of amps marries both tube and transistor amps into one. Usually there are tubes at one stage of amplification and transistors at the other stage (preamp and power amp)

Recently, digital amps were introduced. These amps use computers and integrated circuits to create the various tones in the amps. Usually, there are a number of different types of effects and tons that you can get. These amps are very versatile.

Examples of some digital amps are Vox Valvetronix, Line6, and a few more. These amps are great if you want to play all different types of music with different types of guitars.