According to the Arizal (Sha’ar Hakavanot, 49a) quoting the Zohar (Parashat Shelah), the most valued Aliyot are the third and sixth because, on a Kabbalistic level, contained within them are spiritual lights. On the other hand, The HIDA (Mahzik Beracha, § 282:3), quoting the Arizal, writes that the original custom among Sepharadim was that the seventh Aliya was the most valuable.
Indeed, Rabbi Meir Attia (MiShulhan Avotenu) writes that the custom in Morocco was that when one was to be accorded honor, such as a groom, one would receive the seventh Aliya. In the city of Rabat, the groom would typically receive the last Mosif (additional) Aliya before proceeding to the seventh Aliya. The widespread custom nowadays is in accordance to the Arizal.
Rabbi Haim Benveniste (Sheyere Keneset HaGedola, Orah Haim, § 135) writes that the rank of importance upon whom to accord a valued Aliya is as follows: a groom on the day of his wedding, a groom within seven days after having gotten married, a Bar Mitzvah, a Sandak, a Mohel, the father of a baby being circumcised and finally one observing a Nahala. Therefore, contrary to popular belief, the seventh Aliya was not customarily reserved for those observing Nahalot.
Rabbi Haim Palagi (Yafe Lelev, vol. V, § 2) writes that the sixth Aliya when Matot-Mas’ei are read together, which discusses the banishment of an inadvertent killer to a city of refuge, is very beneficial for one to seek atonement for the sin of wasting seed. The sixth Aliya of Parashat Vaethanan, which discusses a similar subject is also auspicious in atoning for the aforementioned sin.
Summary: The widespread custom nowadays is to seek the third or sixth aliyah. The seventh aliyah was accorded very high honor as well.