Several resources I've looked over define つもり as (often) being used to say "I intend to ~", such as this example sentence from Genki I:
週末にたけしさんとテニスをするつもりです。 "I intend to play tennis with Takeshi this weekend"
To say in English that you intend to do something feels both more formal in register and somewhat weaker than using the simple future "I will ~". Asking about someone's plans for the night/vacation/project/etc is something that comes up all the time, and I absolutely do not hear "I intend to do ~" under most circumstances. That said, Genki introduces this construction quite early, which makes me believe it must be more common in Japanese.
In what situations is it appropriate to say するつもり where it would not be appropriate to say します? Is this a common construction for casual conversation, or is it reserved for more polite and formal situations?