Base36: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ
Good encoding for binary data in textual contexts. Such as where you have parameter inputs or database fields that are constrained and only accept certain characters. The lack of spaces means that it can be used on the command-line easily. Example use: IRC channel names.
Base64: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
Same as above but it adds lower-case alphabet characters. This is important because as you restrict the number of characters allowed in a byte: the length of the string goes up massively. With more characters the coding is more efficient. Example use: YouTube video ids.
Base92: "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz~!@#$%^&*()_+{}\"<>?`-=[];',./|"
Base92 is every character you can make on a standard key-board (I've replaced space with pipe here.) It includes many characters that have special meanings on the command-line or may be used as delimiters in text-based protocols. So while this offers a more 'efficient' encoding scheme for binary data it may break in some contexts. It's best where the input allows for typical formatting. Example use: forum / chat messages.
BaseN encoding schemes are interesting because they allow you to use standard text-fields in many systems to store binary data. The most well-known here is base64 which allows browsers to embed whole files as text and store them directly in the HTML. Some sites use these for optimization hacks.