Freakezette
The true number of Kanji numbers in the many thousands (I think my electronic dictionary claims to have 12,000 or something excessive) but many of these are classical forms or more complicated forms of what's in use today. In 1946, in order simplify things and promote literacy, the government made a list of "Touyou Kanji" (Kanji for general use) and requested newspapers and magazines keep the kanji they use to this list of 1850 kanji. In 1981 the list was expanded to 1945 and that's now called the "Jouyou Kanji" (kanji for everyday use). Everyone is suppose to know these kanji by the time they graduate from highschool.
During gradeschool (1-6 grade) Japanese children learn kyouiku (educational) kanji, which totals 1006 kanji (about 80-200 a year). During secondary school, students learn an additional 939 kanji. There are also jinmeiyo kanji that are not on the Jouyou list and are for use in names. The number of jinmeiyo kanji hovered around 300 for a while, but then jumped to more than 900 in the past couple years. Some of these kanji are not necessarily used in names but are just frequently used words.
Some students choose to learn kanji in the grade school order, which is fine but it should be noted the order that kanji is taught in japan is not necessarily based on frequency but on how easy they are. For example kyuu 弓 which means "archery bow" is taught in 2nd grade, but isn't on the Japanese Language Profitiency Test (a test ment to gauge the profitiency of a foreigner) until level 1 (the highest level). Still, if you go by the grade you can learn kanji in pretty small sets.
Like bakahito said, some kanji have more than one form, one being a classical form. And many words have kanji but aren't used. Verbs like suru (a common verb that generally means to do) and Iru (to exist) have kanji but you don't see them much. Also frequent expressions like "baka" (stupid) "arigatou" (thanks) and "kawaii" (cute) are usually written in hiragana. (even katakana for an added emphasis)
Actually, despite what some may tell you, kana words appearing in,like
arigatou (written 有難う), are not all that unusuall, especially on documents such as bills, orders, etc. So it really does pay to learn your characters, especially, as Freakezette mentioned, the
jyoyo kanji. Knowing some basic characters always helps to make life in Japan a little easier.