There are two biggies here: leukaemia, and lymphoma.
Basically, there's acute lymphoblastic leukaemia (ALL - this is pronounced "AY-ELL-ELL", not "all") and acute myeloid leukaemia (AML). ALL is the biggie in paeds, and there's probably a load more but I'd rather learn about the common ones, to be honest.
Just like leukaemia, there's two basic types based around a bloke called Hodgkin who I assume was pretty damn clever. There is Hodgkin's lymphoma and non-Hodgkin's lymphoma. Presumably, he was pretty badass if he got a whole set of cancers named after him. The former is more common in adolescence, the latter in childhood.
There are a few other nasties to deal with: