To put it simply: European titles generally descend through the male line only, unless the mother is a reigning monarch. There are a few exceptions, but if the father has no title, the children will not either. The father may also hold a title that is not heritable, so his children will be simply "Mr." or "Miss".
Many princesses have married untitled men -- Princess Anne in the UK is one -- and their children are untitled.
It is entirely possible to be in line to a throne but to be untitled. There are plenty of untitled people in line to the British throne.
Should Princess Caroline become the reigning Princess of Monaco -- that is, should she inherit the Monegasque throne from her brother because he has never fathered a legitimate child -- her three eldest children should instantly acquire titles.
Her youngest has a title (though it has no real legal meaning or substance, because German titles essentially became defunct after World War I), because her father is the Prince of Hanover.
I think, by the way, that there's a good chance Prince Albert and his soon-to-be wife will have a child.
Samwise, Prince Philip was a minor Greek prince, not "Crown Prince" of Greece. He was not close to the throne. That's why he had no objection to giving up his Greek title. He did so, so that he became plain Philip Mounbatten. His British titles were indeed gifts of the monarch.