There are many different types of geocache containers. There are no rules for what type of container you have to use if you decide to hide one, however you want to choose a container that is as watertight as possible. Ammunition boxes are a popular choice - they're called "ammo cans" or "ammo boxes" for short. The picture above is of a typical size ammo can, but the little address and mailbox flag are a funny decoration - normally an ammo can is a green color, although sometimes people spray paint them brown or even in a camouflage pattern to make it easier to hide. Often these are used for geocaches hidden in the woods or other somewhat remote areas that have trees, brush, rock walls, etc. where something of this size can be hidden. The ammo can is also nice because there's plenty of room inside for a nice size log book, travel bugs and swag. Other containers can be used however - it's not uncommon to see lock-n-locks, tupperware, gladware, etc., however if you live in an area that experiences cold winters, some plastic containers will crack and let water in. The lock-n-locks seem to be pretty good at enduring all sorts of weather, for a plastic container.
(On the cache page at www.geocaching.com, under the name of the cache, usually the size of the cache is indicated. An ammo can of this size would normally be considered a "regular" size cache. This information is helpful so when you get to "ground zero" and you start looking around, it makes a big difference whether you are looking for a cache the size of an ammo can or a geocache the size of a film container.)
Another popular type of cache hide is what's called a "micro". This is a very small geocache, and often times a film container or hide-a-key are used (though there are lots of other containers that can be used like a pill bottle for example). Micros are popular in urban areas (since there are rarely larger hiding spots available) and they are popular for hides along a highway (there are often hides at rest stops) because the hide-a-keys tuck nicely under or behind a guardrail. Sometimes people will hide a micro in the woods, and geocachers tend to look upon these with disdain - common thinking is that in the woods there should be plenty of room to hide a regular size cache, which is preferable if possible because that leaves opportunities for trades and travel bug and geocoin exchanges. Also, finding a film container in a forest is a lot harder than finding an ammo can! However, micro size caches are often used in stages of a multi-cache and for that purpose in the woods, it's considered acceptable. Generally a micro will only have room for a log sheet and a writing implement - usually no room for swag. Sometimes a cache page will instruct you to bring your own pen if they were unable to fit one in the cache, so be sure to read the cache page carefully.
Here is an example of a micro that is neither a hide-a-key or film container - it contained only a log sheet and pencil. The velcro around the outside attaches to additional velcro in it's hiding spot to hold it in place. There is no end to the clever ideas you will come across.
The last type of cache hide that you will often come across is the smallest geocache yet - a nano. The smallest size indicated on the cache page is "micro" but often in the cache description it may be mentioned that you are actually looking for a nano.
Here is an example of the type of container often used for a nano:
Photo from : http://shop.geoswag.com
The website doesn't give the dimensions, but the geocache above is about the size of 3 large aspirins stacked on top of each other. You might think something this small would be impossible to find, however, these nanos are almost always magnetic, which gives you a big clue as to where it is hidden - look for metal objects. (The white scrolled object on the right in the photo is the log sheet!)
These are common sizes and types of cache containers, but there are no rules as to what can be used, so unless it's specifically mentioned on the cache page, you can't always be sure exactly what you are looking for, however at least the size is usually indicated and that is helpful. Be warned though - now and then you will come across a really clever cache container - like this:
Photo from : http://www.shop4swag.com
Oh yes, you guessed it - it's a fake rock with a cutout on the bottom for a log sheet. Be warned - these are not the norm, but you'll come across some really clever and difficult hides - but that makes it all the more fun and challenging. If you like that sort of thing. If not, there are plenty of guardrail hides to keep you busy for a long time. :-D