In English or Spanish there are possessive pronouns like my, your, her, his, mi, tu, su, etc. that you can use to show possession. For example, my car. But in Japanese the only way I've seen (or that I remember right now) for a phrase like that is with the use of the particle "no". 私の車. Is that the only way there is?
我【わ】が is almost recognized in modern Japanese as a fixed single word that means my. が was a possession marker like の in old Japanese, but this meaning has dropped out of use. Modern dictionaries usually list this as a distinct entry (as a 連体詞). 我らが is similar.
Besides these, I don't think there are common possessive personal pronouns.