Replace the glass in a coffee table by measuring the broken glass within 1/8-inch accuracy and ordering a new piece. It is often easier to draw the panel to scale on graph paper and label each measurement. Make a note of the color, bevel and frosting of the glass so the glass cutter provides an exact duplicate.
Once the glass breaks, you might prefer replacing it with something less fragile than another piece of the same material. One option is to replace the glass panel with a piece of veneer plywood to match the rest of the table. Measure the broken glass just as if you were replacing it with new glass and cut the plywood to the exact fit. Stain the new wood to match the rest of the table and apply a high gloss finish.
Another option is to replace the glass with ceramic tile. The table must be very sturdy for this option. Cut a piece of plywood the same size as the tabletop and attach it with screws. Apply the tile just as you would to a floor or countertop. If you prefer the look of a solid tabletop, have a marble or granite tabletop cut to replace the broken glass.