UTF-8 recently marked the 20th year since its inception (its official anniversary being January 25, 2013), and in celebration here's a brief overview (from Wikipedia):
The first 128 characters (US-ASCII) need one byte. The next 1,920 characters need two bytes to encode. This covers the remainder of almost all Latin-derived alphabets, and also Greek, Cyrillic, Coptic, Armenian, Hebrew, Arabic, Syriac and Tāna alphabets, as well as Combining Diacritical Marks. Three bytes are needed for characters in the rest of the Basic Multilingual Plane (which contains virtually all characters in common use). Four bytes are needed for characters in the other planes of Unicode, which include less common CJK characters and various historic scripts and mathematical symbols. The original specification covered numbers up to 31 bits (the original limit of the Universal Character Set). In November 2003 UTF-8 was restricted by RFC 3629 to end at U+10FFFF, in order to match the constraints of the UTF-16 character encoding. This removed all 5- and 6-byte sequences, and about half of the 4-byte sequences.
And in addendum, here is a list of some of the interesting ones I always find myself having to look up on FileFormat.info's Browser Test Pages: