Android - Can we connect a normal earphone / headphone to a Android device?

The typical audio only jack has 3 rings, usually call Tip, Ring, Sleeve (TRS). These typically map to Left, Right, and Ground. Phone manufactures wanted to make this jack work with existing headphone so they used a connector with 4 rings, called Tip, Ring, Ring, Sleeve (TRRS). These map to Left, Right, and Ground just like the 3 ring, but the final connector maps to a microphone. This makes it so that if you plug an audio only cable into it, the microphone input gets connected to ground so nothing is hurt. It also means that if a headset with microphone is connected to an audio only device, the microphone is connected to ground, also hurting nothing.

Sources:

• What protocol does a headphone jack use?
• Leads Direct: Jack Plugs & Sockets

Yes, a "regular" set of headphones will work just fine, in much the same way that a single-channel earphone works in a stereo headphone jack. The other bits are for the microphone and the controls, but since your headphones won't have those it won't matter.

I have had occasion to use 1st generation iPod earbuds as well as some generic earbuds in my Galaxy Nexus. My daughter uses a pair of headphones I had lying around (that are probably ten years old) in her phone when she's at home listening to music. At worst you may find a channel doesn't work (no sound in one ear) but you don't need to worry about shorting out or damaging anything.

Wikipedia has more information than you could possibly want to know about 3.5mm connectors.