There are 3 major types of inverters - sine wave (or "true" sine wave), modified sine wave (actually a modified square wave), and square wave.
Sine Wave
A sine wave is what you get from your local utility company and (usually) from a generator. This is because it is generated by rotating AC machinery and sine waves are a natural product of rotating AC machinery. The major advantage of a sine wave inverter is that all of the equipment which is sold on the market is designed for a sine wave. This guarantees that the equipment will work to its full specifications.
Some appliances, such as motors and microwave ovens will only produce full output with sine wave power.
A few appliances, such as bread makers, light dimmers, and some battery chargers require a sine wave to work at all.
Sine wave inverters are always more expensive - from 2 to 3 times as much.
Modified Sine Wave (quasi-sine)
A modified sine wave inverter actually has a waveform more like a square wave, but with an extra step. A modified sine wave inverter will work fine with most equipment, although the efficiency or power will be reduced with some. Motors, such as refrigerator motor, pumps, fans etc will use more power from the inverter due to lower efficiency. Most motors will use about 20% more power.
Some fluorescent lights will not operate quite as bright, and some may buzz or make annoying humming noises.
Appliances with electronic timers and/or digital clocks will often not operate correctly. Many appliances get their timing from the line power. Because the modified sine wave is noisier and rougher than a pure sine wave, clocks and timers may run faster or not work at all.
Items such as bread makers and light dimmers may not work at all - in many cases appliances that use electronic temperature controls will not control.
Square Wave
Very few but the very cheapest inverters any more are square wave. A square wave inverter will run simple things like tools with universal motors with no problem - but not much else.
Taken from :
http://www.windsun.com/Inverters/Inverter_selection.htm