I disagree with the above interpretations of the sense of this phrase.
Although on a superficial level wants is in the present tense and wanted is in the past tense, there is an important shade of meaning that has nothing to do with the tense.
Consider the following phrase:
I wanted to see if you could help me.
While this certainly could refer to a past desire that I no longer have, it is much more probable that I am using the past polite form. This is common in many modal verbs.
Thus, in the example you gave, a lot depends on context:
Tom wants you to pick him up.
This unambiguously refers to what Tom wants now, but depending on your tone of voice can come off as impolite.
Tom wanted you to pick him up.
This can refer to a past desire, but to my (American) ear sounds much more polite and hesitant, as if he did not have the right to expect you to pick him up.