There have been some interesting questions at eGullet lately regarding the different chilies used in Thai cooking. This is by no means an exhaustive list of all the chilies used in Thailand, but the five below are by far the most commonly used. I've tried to describe what they look like, how they're used, and their spiciness.
The most commonly used chilies in Thailand are undoubtedly phrik khii noo, literally, "mouse dropping chilies":
These are generally also the hottest chilies in Thailand, and can range from tiny in size (as pictured above), to almost 2-3 time the length shown above. They are used in almost every conceivable way: ground up in curry pastes, smashed up and added to stir fries, smashed up and added to soups or salads, or used in nam phrik, Thai-style "dips". Dried phrik khii noo are used in curry pastes to add a spicy taste.
Another common kind of chili are phrik chii faa, literally, "pointing at the sky chilies", apparently for the way they grow:
Phrik chii faa generally range from mild to slightly spicy, and come in three colors: green, red, and orange. They are most commonly used as a garnish. They can be sliced into rings and preserved in vinegar as a condiment for noodle dishes, or sliced or julienned and used to garnish curries such as kaeng phanaeng. Sometimes they are used fresh in curry pastes, but this is generally to add color or body, rather than spiciness.
Another chile that is most commonly used as a garnish are phrik yuak:
These are usually mild, and are almost always the pale green color shown above. Sliced, they can garnish a variety of dishes, and are especially popular in Thai Muslim cuisine, where they are somtimes stuffed with fish and steamed or boiled.
can at times be the spiciest Thai chilies of all. They are recognized by their yellow and orange colors (although they are normally somewhat shorter than the ones shown above). They are eaten fresh in some northern and northeastern Thai dishes, but are more commonly dried:
and ground up to be taken as a conidment with noodle dishes.
are almost exclusively associated with the northern Thai dish, nam phrik num. This dish sees the chilies grilled along with shallots, garlic and tomatoes, and then pounded together into a spicy "dip". The chilies are typically longer than phrik chii faa, and can range in spice from hot to very hot. In northern Thailand, they are often a darker shade of green than shown above.