There are probably as many kinds of workbenches as there are woodworkers. However, when it comes to the base, there do seem to be two "kinds" of woodworkers: Those who leave the base empty, and those who build in drawers or cabinets.
I'm in the second camp.
My reasons were for weight and storage. First, I wanted to increase the weight of my bench. I make regular use of handplanes, and a heavy stationary base is very helpful when planing. Storage is kind of an obvious reason. I have a small shop, and need to make good use of the available space. Also, by having storage right in the base of the bench I hope to also be able to work more efficiently, by having frequently used tools and items close at hand.
I made the drawer unit carcass out of plywood. I made it to slip in and out of the base. If I ever do move, I should be able to take it out as a unit, to lighten the bench. It is simply secured to the bench at the back with a few screws. In one of the photo's below you can see it partly protruding from the bench.
The drawers themselves are from half inch poplar, of a simple rabbet and glue construction.
I did have some fun with the faces of the drawers. I resawed some walnut that I had available and planed it down to about a 3/8" thickness. This was then attached to the faces of the drawers to dress things up a bit. I also could play around a bit with some bookmatching of the pieces.
The bottom drawer is much larger than the top three, to hold some power tools. To make it blend in with the faces of the other drawers, I attached it's face in three separate parts, with a small gap between each piece.
I originally intended to purchase some handles. I wanted some fairly large handles, for looks and utility. I found myself interested in these large/long stainless steel bar handles. Unfortunately, the cost of about $8-10 each seemed more than a little excessive for shop handles. After a bit of thought, I realized that I could make something quite similar with just a bit of work. I had a four-foot maple dowel laying around, half-inch thick, which I cut into four pieces. Then I cut some maple scraps for the ends, and drilled a hole in each with a forstner bit to receive the dowel. A bit of glue, a bit of measuring, a bit of drilling, a few woodscrews, and voila.