Here are some of the types of kitchen sinks avaiable:

Undermount
stainless steel sinks - the most common material used for sinks, stainless steel is easy to clean, hygienic,durable, and not expensive

Topmount stainless steel sinks

Acrylic sinks - very resistant at scratches, can be painted in any color to match your kitchen.

Cast iron sinks - the cheapest, this material is not scratch resistant, spots of water can appear, even rust

Copper sinks - doesn't rust or corrode; if left unpolished, develops a patina over time, and scratches more easily than stainless steel and other materials

Granite sinks - easy to maintain; softer granite can stain or etch, and it is expensive

Stone sinks - look good, but are also resistant at all kinds of shocks. The only drawback for some people would be the high price.