-san : generic politeness. Mr., Miss., Ms. Like in English, it's more formal when paired with the surname, but unlike English, it doesn't sound weird next to the first name (Miss Arashi versus Arashi-san).
-chan : an affectionate dimunitive used on small children and girls; most boys above the age of ten would be put off to have it used on them. It gives a "cute" feeling to the name, which not everyone likes. Yuzuriha is refered to as Yuzuriha-chan, Hokuto is Hokuto-chan. Arashi would be embarrassed to be called such.
You *can* use it on boys, but you'd better be close to them, and they still might find it embarrassing. Consider, though, that Sorata's favourite way of introducing himself is "Sora-chan," and he refers to himself as such when joking around; Seishirou in Tokyo Babylon is called "Sei-chan" by Hokuto. It depends on the closeness of the relationship and the sense and humor of the boy; Sorata probably would be put off if someone called him that seriously.
-sama : super polite -san. It can be translated as "lord" or "lady," and usually is, but there's a higher level word for that which works better. It's super polite, though, which is all you need to know.
-dono : Lord or Lady. This can be used in less formal contexts, but it's the most polite honorific you're likely to run into.
-kun : Kun is actually really complicated. The other commenters are right in saying it's a diminuitive used on boys, but that's not all; it's also a less formal version of -san, depending on context. A woman might call her male co-workers [surname]-kun; she's being polite but still showing herself as equal level to them. A girl might be called [name]-kun (in fact, in Furuba, several people call Tohru "Tohru-kun"), which isn't affectionate, just a slightly more casual way of saying "Tohru-san."
But it *can* be used affectionately on boys (mostly); Aoki uses "Kamui-kun," and several people refer to Sorata as "Sorata-kun." They're being polite, but still showing that they like them - -kun is complicated, though, so don't sweat it much. Just remember that it's a less formal "-san," and can be used as an affectionate diminutive.
In Furuba, you also might see "senpai" and "kohai" - those simply mean "upperclassman" and "underclassman," respectively.
There's also - and this is actually the most important - the *lack* of honorific. In Japanese, to call someone by no honorifics at all implies a certain closeness to the person (or rudeness). So Kamui going around using no honorifics implies his sort of rude speech patterns; Sorata calling Arashi by her first name only implies that they are in a very close *cough* relationship. Understandably, not everyone feels comfortable being addressed as such, especially by people they aren't so close to.
There's also the difference between first name and surname, which is similiar - not everyone feels comfortable calling the other by first names, but of course it depends on their personal speech patterns as well. Tohru uses "Sohma" on Yuki, so he'd be surprised if she suddenly called him "Yuki," but Kyo - being a relative and rude to Yuki - just uses "Yuki".
With X explanations since you know the characters:
-san : generic politeness. Mr., Miss., Ms. Like in English, it's more formal when paired with the surname, but unlike English, it doesn't sound weird next to the first name (Miss Arashi versus Arashi-san).
-chan : an affectionate dimunitive used on small children and girls; most boys above the age of ten would be put off to have it used on them. It gives a "cute" feeling to the name, which not everyone likes. Yuzuriha is refered to as Yuzuriha-chan, Hokuto is Hokuto-chan. Arashi would be embarrassed to be called such.
You *can* use it on boys, but you'd better be close to them, and they still might find it embarrassing. Consider, though, that Sorata's favourite way of introducing himself is "Sora-chan," and he refers to himself as such when joking around; Seishirou in Tokyo Babylon is called "Sei-chan" by Hokuto. It depends on the closeness of the relationship and the sense and humor of the boy; Sorata probably would be put off if someone called him that seriously.
-sama : super polite -san. It can be translated as "lord" or "lady," and usually is, but there's a higher level word for that which works better. It's super polite, though, which is all you need to know.
-dono : Lord or Lady. This can be used in less formal contexts, but it's the most polite honorific you're likely to run into.
-kun : Kun is actually really complicated. The other commenters are right in saying it's a diminuitive used on boys, but that's not all; it's also a less formal version of -san, depending on context. A woman might call her male co-workers [surname]-kun; she's being polite but still showing herself as equal level to them. A girl might be called [name]-kun (in fact, in Furuba, several people call Tohru "Tohru-kun"), which isn't affectionate, just a slightly more casual way of saying "Tohru-san."
But it *can* be used affectionately on boys (mostly); Aoki uses "Kamui-kun," and several people refer to Sorata as "Sorata-kun." They're being polite, but still showing that they like them - -kun is complicated, though, so don't sweat it much. Just remember that it's a less formal "-san," and can be used as an affectionate diminutive.
In Furuba, you also might see "senpai" and "kohai" - those simply mean "upperclassman" and "underclassman," respectively.
There's also - and this is actually the most important - the *lack* of honorific. In Japanese, to call someone by no honorifics at all implies a certain closeness to the person (or rudeness). So Kamui going around using no honorifics implies his sort of rude speech patterns; Sorata calling Arashi by her first name only implies that they are in a very close *cough* relationship. Understandably, not everyone feels comfortable being addressed as such, especially by people they aren't so close to.
There's also the difference between first name and surname, which is similiar - not everyone feels comfortable calling the other by first names, but of course it depends on their personal speech patterns as well. Tohru uses "Sohma" on Yuki, so he'd be surprised if she suddenly called him "Yuki," but Kyo - being a relative and rude to Yuki - just uses "Yuki".
:D