Why is Bitcoin address encoded in base58? Why does bitcoin address encoding use base58 instead of, for instance, base64? I don't see it is useful in any way.
Why base-58 instead of standard base-64 encoding?


Don't want 0OIl characters that look the same in some fonts and
 could be used to create visually identical looking account numbers.
A string with non-alphanumeric characters is not as easily accepted as an account number.
E-mail usually won't line-break if there's no punctuation to break at.
Double-clicking selects the whole number as one word if it's all alphanumeric.


Features of Base58Check


An arbitrarily sized payload
A  set of 58 alphanumeric symbols consisting of easily distinguished uppercase and lowercase letters (0OIl are not used)
One byte of version/application information. Bitcoin addresses use 0x00 for this byte (future ones may use 0x05).
Four bytes (32 bits) of SHA256-based error checking code. This code can be used to automatically detect and possibly correct typographical errors.
An extra step for preservation of leading zeroes in the data