Typically, you capitalize all the forms derived from the 2nd person pronouns “ty” and “wy”. This includes personal pronouns in all grammatical cases (“Cię”, “Was”, “Ciebie”, “Wami”, etc.), as well as the respective possessive pronouns (“Twój”, “Wasz”, “Twoją”, “Waszymi”, etc.).
The reflexive forms—both personal (“siebie”, “sobą”) and possessive (“swój”, “swoich”) are never capitalized in the middle of a sentence, regardless of whom they refer to. The rule of thumb here is that when you address someone directly, you might want to capitalize the pronoun to show your respect for the person. Reflexive pronouns are not very direct compared to regular pronouns, hence they are never capitalized.
There is another group of words that function as direct forms of address—the formal “you” pronouns such as “pan”, “pani”, “państwo”. As you know, the very purpose of formal pronouns is to give the person the respect that is expected in a formal setting, so it is only logical that they would also be capitalized when put in writing. So if you’re addressing a person you’re not on familiar terms with in a letter or an e-mail, you should always capitalize the pronouns—“Pani”, “Pan”, “Państwo”—in the middle of a sentence.
Note that this is different from using these words as normal nouns, as in “Tamta pani to moja ciocia” (“That lady is my aunt”)—here you are not expected to capitalize the word (since it’s not even a pronoun).
Finally, you will sometimes capitalize third person pronouns (“On”, “Ona”) when they refer to divine beings, royalty, or someone who is very important to you. But this is really a fringe case.
And of course, you are often expected to capitalize some formal titles etc. (from Profesor Nowak to Jego Wysokość [“His Majesty”]), but there isn’t really that much difference between Polish and English in this respect. Some companies even like to capitalize “nasi Klienci” in their marketing copy, which I find a bit over the top.