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In Japanese, "chan" is generally described as:
ちゃん
(接尾)
(サンの転)
人を表す名詞に付けて、親しみを表す呼び方。
「和子－」「おにい－」
(suffix)
(derived from "san")
Attached to a noun representing a person to indicate intimacy when addressing that person or saying their name.
Examples: Kazuko-chan, oniichan (older brother)
Source: Koujien 4th ed. Translation by myself.
The usage of -chan is perhaps one of the most misunderstood aspects of functional Japanese among students. This is probably because most high-school and university textbooks don't normally touch the subject. This is a very odd omission, considering that -chan continues to be used throughout life, and is very important for use in all sorts of social circles.
In addition to being a diminuitive used by adults to address small children, -chan is used by small children when addressing pretty much everything. Parents are kaa-chan (mommy) and tou-chan (daddy). nii-chan (older brother) and nee-chan (older sister) are not only used for family, but also for any young man or woman. (Note that the honorific o- is often used in conjunction, as in onee-chan.)
This suffix can even be used when children are completely uninvolved. It is often used among close friends, even adults, especially women. It's not uncommon to find at least one "chan" in every Japanese office -- usually the youngest female employee.
In the media, -chan as a suffix for small children in newspaper articles, TV, and radio news. It used to be used well into elementary school ages, but lately, it is being phased out in favor of -san (for girls) and -kun (for boys) starting as young as grade 3.
-chan is often used for nicknames, especially with shortened or changed names, as in Nozomi / Non-chan. It's not unheard of for famous people to be referred to by the media and public in this way. Recent examples include Q-chan (marathon runner Naoko Takahashi) and Yawara-chan (judoka Ryoko Tamura). You needn't be female, or even cute -- Arnold Schwarzenegger is commonly known as Shuwa-chan to Japanese audiences. Let's not forget fictional characters, such as Crayon Shin-chan, Chibi Maruko-chan, and the ubiquitous Kitty-chan (née Kitty White.) Note that this usage is not exclusive to -chan, other suffixes such as -kun, -ko, -han, or no suffix at all are often used.
Common uses include not only people, but also pets, and sometimes personal possessions, such as cars. (My friend calls her Honda Logo "Rogo-chan".)
It also has defacto use as a diminuifier in some compound words, such as "akachan" (baby) and "Botchan" (Young Master).
In Japanese baby-speak, "chan" often becomes "tan".
"chan" is also a variant pronunciation of "chichi" (father), a Japanese reading of the Chinese "Tang" 銭 (as in the dynasty), as well as chian turpentine (a Chinese type of pitch). It's also a common Japanese reading for certain Chinese and Korean family names. (Yes, in this case, they are "Chan-san.")
By the way, the character used for "zen", 禅, is also "chan" (rising tone) in Chinese. This word originates from the Sanskrit "dhyāna", or "meditation".