Fortunately I've only had a few minor crashes on my road bike and you’ll find minor crashes are mostly down to just going too sharp and too fast around a corner. As I’m going down on my bike the first thing I tend to think is ‘OH SHIT NOT MY BIKE!’
If you do crash, providing you have made certain you've sorted yourself out first, you may find your bike is damaged. Commonly your shifter(s) might be bent - don’t panic this can be easily straightened by using a 5mm allen key to loosen the shifter clamp, which is under the rubber covering, this means you can re-position your shifter and then re-tighten at the correct position.
The wheel(s) may be buckled- this means the rim basically goes all wobbly. You can tell it has done this by turning your wheel and watching how close the brakes go to the rim. If you just need to get home loosen the brakes and be cautious going home as braking performance will be reduced. After this you can either find a guide to 'true' the wheel yourself or go to your local bike shop to have it done for you.
If you have a carbon frame it can be at risk of cracking or indeed snapping. Before you ride your bike again check it over for any cracks in the frame, however small. These can develop into larger cracks then indeed completely snap when later riding!
The gear hanger and derailleur.
The gear hanger is a piece of weaker metal that means if the right hand side of your bike comes down damage is minimised. Instead of your frame bending or breaking the gear hanger is designed to take the impact. When this does happen the hanger will bend- meaning that gear shifting will be impaired. To tell if your hanger is bent view it from the rear of the bike, it should hang vertically and not twisted. You can try to fix this yourself by bending it back into position yourself with a pair of pliers, however this is unlikely to get you back to completely accurate shifting. A hanger alignment tool can be used to correct the alignment of your hanger with precision, but can be costly so replacing the hanger is probably going to be the cheapest and easiest option. Ensure you get one that is compatible and use your old one as a template.
This is by no means an extensive guide to what could be broken on your bike, only common problems. Take your bike to the local bike shop to have it checked over if you are un-sure it is rideable or you are un-comfortable making repairs yourself.