It used to be that when someone got an aliyah, they would read their own Torah portion, and not have it read for them by the ba'al kriyah. This practice seems to have fallen by the wayside, as every synagogue I've been in has had a ba'al kriyah -- (almost) no one will read their own aliyah, except for certain minyanim where the kriyah is split up, and the gabbai will give each ba'al kriyah an aliyah...which is still not the same as "having each oleh read their own aliyah."
Are there any modern-day communities where the custom is still to have each oleh read their own aliyah?