In Star Trek, how many times has
been demanded by anyone other than Picard? I'm looking for a complete list.
The question is not necessarily exclusive to the The Next Generation.
I won't force you to read the whole answer as it is a little bit long, so to cut to the chase:
Well, you said you wanted a complete list, so here goes:
QUARK: Go ahead, kill me. That's why I'm here, isn't it, to be killed? Well, here I am, so go ahead and do it. You all want me to pick up that sword and try to fight him, don't you? But I don't have a chance and you know it. You only want me to put up a fight so your precious honour will be satisfied. Well, I'm not going to make it so easy for you.
and again in 'The Maquis Pt II':
QUARK: Then I'll make it so simple that even a Vulcan can understand.
DUKAT: Basso! That's enough. Welcome to Terok Nor. I hope your stay here will be a pleasant one. I assure you, I will do everything possible to make it so.
WORF: And while you dispose of the Intendant, I will dispose of the rebels. Make it so!
HROTHGAR: Always with you it is time to sleep. Perhaps you have forgotten that the work of a warrior is battle not rest. You would do well to learn from Lord Schweitzer. This was a beautiful hall once, before Grendel. You will make it so again. You have our thanks.
PLASUS: We'll do everything possible to make it so. Come, gentlemen.
JAMESON: A sensible precaution, Picard. Make it so.
and special mention to Picard Jr in TNG 'Rascals'.
From the above, it's fair to say that Riker says it a lot!
However, that's just the number of times the phrase has been used, not the number of times it has been demanded. From the above list, 11 of those are actual demands using that phrase. To get to that figure, I have included:
which = 11
Ignoring cases where a character said the sequence of words but not the phrase itself with same meaning (example "I'm not going to make it so easy"), we have
Riker, in "Contagion", "Best of Both Worlds Part 1", "Best of Both Worlds Part 2" (twice), and "Darmok"
Data, in "Gambit Part 2"
The above cases are heavily influenced by Picard. The following one isn't, however, as far as we know, since it comes from Worf in the Mirror Universe (where we don't know of Picard's existence, the Terrans are weak and slaves, and Worf as Regent most certainly never served under Picard):
Worf, in DS9's "Shattered Mirror".
There are three more, pointed out by N_Soong. I don't mean to steal them, but now that I know about then, I don't see how I can not edit them in here. Please give him an upvote too.
La Forge in "Angel One"
Riker, in "The Battle"
Data, in Generations.
I was going to edit in the quotes, but it doesn't add much, in my opinion since the quote in all cases is
Make it so
(duh) with essentially the context not adding much.
That is ten times, by my current count, but there may be a few more.
Honorable mention in "Samaritan Snare", I believe Grebnedlog was just too dumb to get it right:
GREBNEDLOG [on viewscreen]: Things to make it go.
RIKER: We will use our tractor beam to tow you to the nearest base.
GREBNEDLOG [on viewscreen]: He can make it go.
Additional side remark which doesn't answer the question but is fun: Capt. Jellico's pseudo-equivalent is Get it done, which he says twice in one episode and only to Riker who he thinks is not "a particularly good first officer."