When building a bookshelf (or other shelving) that will need to support a considerable amount of weight, a single 3/4-inch thick piece of plywood or other stock may sag in the middle after a period of time. Fortunately, if you know that the shelves will need to support a considerable amount of weight (perhaps upwards of a couple hundred pounds), here are a couple of woodworking ideas for super-strong shelves you can consider.
One idea is to employ an edge similar to a breadboard edge (as used in these free woodworking plans for a hardwood cutting board. This is basically a tongue-and-groove joint where the tongue is cut on a piece of hardwood that will fit into a groove in the edge of the shelf plywood. The plywood is wrapped on all four sides with this tongue-and-groove hardwood edging, using 45-degree mitered corner joints. This tongue can provide a considerable amount of strength to a shelf, although it can be a bit time consuming. Also keep in mind that if you intend to stain the shelves, the hardwood you choose will stain to a different color than the plywood, so you'll likely want to make this a design feature and accentuate the differences in the colors of the wood as you design the piece.
Another idea that would be more expensive, but far simpler is to simply sandwich two layers of 3/4-inch plywood. This idea should probably be avoided if you're choosing to use hardwood or dimensional lumber, as the expansion/contraction will likely cause undue stress on the glue joint between the two layers.
However, it is ideal if you intend to use two layers of plywood. Simply apply a thin, even coat of a quality woodworking glue to all of the mating surfaces and press together, holding the sandwiched layers with clamps until the glue dries.
Once the glue has dried, remove the clamps, scrape off any excess glue that escaped the joint and trim the exposed face with a piece of 1x2 in the wood of your choice. The 1x2 can be attached using biscuit joinery.