Body shapes are simpler. The basics are easily recognizable. Still, there are some fringe cases where it's hard to identify the style properly. There is also sub-classification, not terribly official, but nonetheless useful.
- The classic car shape is a sedan. This is a car with four doors and a separate boot - a luggage compartment that opens separate from the glass above it. Note that the boot doesn't have to be in the back (cf old rear-engined Skodas) and doesn't even have to be horizontal; the original Mini was actually a two-door sedan, because it had a bottom-hinged luggage hatch that did not extend to the rear window. Also, a sedan is not necessarily a distinct three-box shape; if you think of the classic Saab 900 coupe, there was barely a transfer from roofline to trunk lid.
- The sporty version of a sedan is a coupe. This has a separate boot and minus two doors; if you want to be strict, there is a distinction between a coupe and a two-door sedan. The latter has the same interior space as a four-door, whereas a coupe is a 2+2 at best. A great example of a two-door sedan is a BMW E30 (the 80s 3-series), whereas the succeeding E36 had severely less rear seat space. Basically, if it looks like they just erased the rear doors, it's a two-door sedan; to be a coupe, it has to look like it was designed like that from the ground up.
- In smaller segments (C and below), the most popular bodystyle is the hatchback. Essentially this is any car that has three or five doors and is shorter than the equivalent sedan. Here you have a set of subclassifications. The classic hatchback is a MkIII and up Golf, with the tailgate close to vertical. If the rear window slopes, then turning into a dropoff sheet of metal, it's called a liftback - the term was, to the best of my knowledge, introduced by Toyota with the bug-eye Corolla of the 90s, which in five door guise had a very different trunk solution compared to the three-door. There is a subtle difference between this and the notchback which, as you may guess from the name, has a notch in the trunk line; the most obvious notchback shape is the Skoda Octavia, which actually looks like a sedan more than anything else.
- The estate, aka station wagon, is distinguishable from the classic hatchback through length - it tends to use the floorplan of the sedan, and in some cases (like the new Opel Vectra) is actually longer than that. You can get confused sometimes as to whether a car is a hatchback or an estate, recently with the Kia Rio; however, because that car is demonstrably shorter than the sedan, it cannot be an estate.
- The fastback is properly a type of hatchback; the problem is that a lot of sports cars these days have tailgates instead of bootlids. It would be improper to call them three-door hatchbacks, so this term has been adopted for things like the Hyundai Coupe/Tiburon, and the upcoming Jaguar XJ. Basically the difference between a notchback and a fastback is the same as the difference between a two-door sedan and a coupe.
- The shooting brake is a rare breed these days, especially with the demise of BMW's metal-top Z3. It is a coupe with a raised glasshouse, a gentleman's touring car intended to carry enough luggage for a fortnight's blast around the continent. It doesn't even need more than two seats, or 2+2 at best. It's meant for speed, not space - and it's coming back; there are reports that the next-generation Audi TT will in fact be a shooting brake.
Now, there are fringe cases not covered by these increasingly specific guidelines. One such is the Mazda RX-8. Yes, technically it has four doors; but because you cannot actually open the rear ones independently, I'm willing to give it a little leeway and recognize it as a coupe. Especially since it is a proper sports car.
Oh, and for all my American readers, a clue: it is not pronounced 'coop'.