As far as arcade games are concerned, a cocktail glass is the surface of a cocktail table. A cocktail table is a small arcade game in the form of a glass topped table. They were very popular from the mid 70s to around 1984. I don't think any new ones have been made since then, but old ones are still around in abundance.
The glass on a cocktail table is often the item most likely to get damaged in some way or another. These rarely actually get broken because they are always made out of very strong safety glass. What is more common is for the top of the glass to get all scratched up, and for the paint underneath the glass to start bubbling and peeling off.
Light scratches on top of the glass can often be repaired using automotive paint buffing compound, or glass polishing compound (if you can find it). Start by doing a little section by hand, if it starts clouding up, then stop, and go get some other kind of polish. If your scratches are really light, then you might be able to get them all out by hand. If not, then you can get a buffing wheel attachement for your drill to make the job a little easier. No matter how you do it, you need to go easy on it, you don't want to over polish it, you just want to remove the scratches.
Peeling paint underneath the glass can be a much more difficult issue to deal with. It all depends on exactly how the glass is painted. Some of them aren't painted at all (like most Sega cocktails).
Begin by removing the glass from the table and carefully cleaning the underside of it. If you have a complicated design then you are going to have to scrape off paint flakes of each color and go to the paint store and get them color matched. If you are lucky, then the majority of the glass will be simply painted black, in that case just get yourself a can of black spraypaint before beginning the next step.
Now you need to remove all the loose paint so your repairs will actually last for a while. Get yourself a razor blade and scrape it lightly over the paint. This should dislodge any loose flakes of paint. Now if you are dealing with a mostly black table (like my Time Pilot), then you can simply scrape off almost all the paint except for the area bordering the monitor, and the areas bordering the other graphics. Once the loose paint is gone you are ready for the next step.
Now for the touch up. If you are only repainting a bunch of black then you can simply mask off the center area where the monitor shows through, and then just paint the entire thing. Painting glass is surprisingly easy. It might run horribly and look terrible on the side that you paint, but if you look at it from the other side you will see a perfectly smooth black finish. If you are repairing a complicated design, then you get to painstakingly recreate the missing graphics using tiny paintbrushes (plan to spend a long time doing that).
Ack, I blew my top!
Sometimes you need to replace the glass entirely, as they do go missing from time to time (or even get broken). If your machine has majorly rounded edges, then I suggest making a cardboard template of the top of the machine to take to the glass shop. Otherwise you just need to measure the top of your machine and remember to ask for rounded edges. The exact thickness varies from table to table, you can usually just ask in the rec.games.video.arcade.collecting newsgroup, and someone will end up measuring theirs and letting you know.
When you actually go to the glass shop, you need to make it very clear that this glass is being used as a table top. If they just cut you any old stuff, then it is going to break. I know that from experience.
For the lazy
Owners of Pac-Man, Ms. Pac-Man, Galaga, and Galaxian machines can order new graphics to apply to the underside of their glass. They are not exactly cheap, but they certainly do look nice. You have to scrape off all the old paint in order to install these graphics kits. I do mean all of it, you can't even leave a speck of paint, or the graphics will end up with an air bubble in them.
For the cheap
If you don't want to spend an arm and a leg on new glass, then you can also use plexiglass as a replacement on some tables. It won't look as nice, and it will scratch easily, but it is really cheap. This works best on the older model tables that don't particularly have rounded edges or overhanging areas.