How many non-Doctor regenerations have we seen on-screen?

Question

Regeneration in Doctor Who was a device created to explain the recasting of the main character, the Doctor himself. But it's something all Time Lords are capable of, and occasionally we've seen Time Lords other than the Doctor regenerate on-screen. E.g. the Master has regenerated once on-screen, and an unknown number of times off-screen. My question is:

how many regeneration events, other than the Doctor's, have appeared on-screen?

_{Main canon only (as far as such a thing exists in Doctor Who): the TV series, Old and New, plus the McGann film.}

Answer 1

Not many

• Although the actual regeneration isn't shown on-screen, in "Planet of the Spiders" we see that the Doctor's old mentor K'anpo Rimpoche has regenerated into Cho-Je, a character introduced earlier in the story^{1, 2}

• In "Destiny of the Daleks", we see Romana "trying on" various regenerations, although the actual regenerative process is not shown on-screen, until she eventually settles on the body played by Lalla Ward:

• The Master (Jacobi to Simm) in "Utopia"

• Melody Pond to Mels in "Day of the Moon":

• Mels to River Song in "Let's Kill Hitler"

• The Time Lord General in "Hell Bent"

• A debateable one³, but K-9 sort-of regenerates (it's referred to as being caused by a "regeneration unit") in the first episode of his 2009 series:

Finally, though not really a regeneration, it seems worth mentioning that we see the Master taking over a new body in "The Keeper of Traken":

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¹ Wibbly-wobbly...

² Nod to Elliot Frisch for reminding me of this one in comments.

³ As John Sensebe points out in comments, K-9 isn't a BBC-licensed show, so it occupies a weird canon-space. I'm inclined to leave it, though, mainly because I think it's funny.

Answer 2

If you only count on-screen regenerations, there have been five:

• River song regenerates twice, in "Day of the Moon" and "Let's Kill Hitler"
• The Master regenerates on-screen once, in "Utopia"
• An anonymous guard regenerates in "Hell Bent"
• In classic Who, a Time Lord named Azmael commits suidice by regeneration in "The Twin Dilemma". (This one is debatable -- he doesn't actually regenerate, he dies by forcing a regeneration when he has none left.)

We know the Master regenerated several other times, but not on-screen. Romana also shows up in a number of forms, but the regenerations always happen off-screen.

Also of note, as of "Day of the Doctor", we have seen all of The Doctor's regenerations on-screen. The regeneration sequence from Eight -> War -> Nine was originally not shown, but "Day of the Doctor" and "Night of the Doctor" fill that gap.