Trying to keep the planets straight is one of the hardest things in GRoY. The planets are continually rising, setting, or being renamed through the whole era. There are originally at least 10, and only 7 remain in 'modern' (circa 1621 S.T.) Glorantha (and not all of the modern ones were among the 10). There are also other bodies that would be thought of as planets on our world, but are not 'planets' by the Gloranthan definitions - most obviously, the 'Jumpers' (which behave similarly to the way planets closer to the sun than earth do). These bodies are largely excluded from discussion.
First, we'll list the modern 7 planets for reference, using their solar names, with the Orlanthi names (from Elder Secrets) in parentheses. There are two paths that the planets travel on. They either follow the path of the Sun, or travel along a path to the South.
SunpathThere are definately some interesting things just comparing these lists. The identification of Uleria and Mastakos with the same star must be a problem for prospective God Learner astrologers, for a start. But the God Learners have a success with Shargash - both are deities of Love and Death, though with a decidedly different emphasis.
The Original Ten Planets according to PlentoniusThis is the planets according to Plentonius on the Gods Wall. There are quite a few things that are pretty certainly wrong here. Another thing that should be noted - eight of these are 'sons of Yelm', and the other two are not. The two that are not sons of Yelm are the first and the last, Zaytenaras and Ghelotralas. Ghelotralas is the messenger to below, and corresponds to Lodril. Probably Zayteneras is another brother of Yelm.
Some Errors/ Problems: Veritherusas is elsewhere mentioned using the feminine form, Veritherusa, so may be female rather than male. Also, elsewhere (in the Ancient Celestial Runes section) Deumalos is said to be a name for Lodril in the sky, and is given the rune given to Ghelotralas by Plentonius, so there is a mistake in one of the other (and I suspect Plentonius is less reliable). Another oddity is that there is another planet on the Gods Wall, Entekos (GW-II-1), who is not described as a planet in the GW writeup. She appeared before the Eight Sons.
GRoY also talks about Dendara as a planet. This is the same planet referred to elsewhere as Entekos. As the introduction to the Entekosiad makes clear, the goddess worshipped as Entekos in Carmania/Pelanda is worshipped as two separate goddesses by the Dara Happans, Entekos and Dendara. The general theory about this is that the cult of Entekos is a cult of female power, and splitting it into two and raising up the servile Dendara removes the threat to the Yelmic patriarchy. This explains a few inconsistencies in GRoY - such as Entekos on the Gods Wall having the planet symbol above her head, and Dendara not, as the Gods Wall probably dates from before the separation of the cults.
Anyway, after the initial (Perfect Sky) situation, with 8 or 10 planets, what happens to them all? Well for a start, about half of them are known by other names at various times, which makes things very confusing. Basically, all of them either disappear, some of them temporarily, some permanently. The best sources for what happens to them are the record of risings near the start, and the Heavens Corrupted (IP pg 88-89).
The Ten Planets and what happens to themSo of our original planets, Falsoretus, Derdurnus, Veritherusas, Deumalos, Buserian are all destroyed or no longer visible. Also, at least one of these (I think Reladivus) becomes Kargzant, which is also no longer visible in modern times. Of eight, there are the two remaining,. One is Shargash. The last remaining one is the bat planet, which continues into modern times (NB: the Crimson Bat is a possible connection - both are red). It is never said which of the original planets is the Bat planet, but neither is its rising recorded separately. If it is one of the original planets, it might be Ghevengus. Lokarnos and Uleria rise as recorded. Dayzatar also disappears (the actual body sets, mythologically then goes up the outside of the dome, rather than descending into the underworld).