2001 Monoliths appear in......

[The Yosemite Bear]

in several Sci-Fi franchises, as per the original they seem to be invisible to remote electronic survalience, they can evolve life near them, oh and someone actually traveling into one in an EVA suit may be turned into a god like being.

So what does:
StarTrek Federation
StarTrek: Other Factions
nBSG colonials
nBSG cylons
40k Imperium
40k Eldar
40k Chaos
40k Tau
40k Necrons
oBSG Colonials
oBSG Cylons
B5 humans
B5 centari
B5 Shadows
B5 Minbari

etc

do with the damn McGuffins?

[NecronLord]

Almost all would study it to see where it came from. Chaos would probably shoot it out of a nova cannon at something, given how impervious they are, or try to possess it for use on the Imperium.

[Batman]

Um-they're NOT invisible. You can absolutely see them (d'uh), you can measure their dimensions, you just can't analyze their interior.
As for what the given SciFi factions would do with it, I don't think any of them has the means to get past the 'Um-we have no fucking clue' stage (yes, I know they managed to hack TMA-3 in 3001 but that was with Bowman actively aiding them).

[The Yosemite Bear]

I was figuring one way or another there would be more starchildren running around each universe...

that may or may not be good.

[Brother-Captain Gaius]

The Ordo Xenos would take quite a lot of interest in it, I'm sure. If/when it's discovered that it's responsible for uplifting new xenos and/or plans to destroy mankind to make room for new species, then I'm sure the Imperium will do what it's best at and annihilate the monolith as only 40k can.

The Orks will take a far more interesting approach, I think:

"Oi, what's dat?"

"Dat's Gork."

"No it isn't you sod! Dat's Mork."

"Shaddup you gits! It's both. So we'z gonna make it look real Orky."

The Orks industrially 'modify' the monolith with their trademark brand of mechanical 'expertise'. Curiously, the Orks don't seem particularly perturbed by its more eldritch qualities, or even really notice them in the first place for that matter. Finished, the sterile black slab is adorned with skulls, glyphs, checks and dags, blotches of red paint, and most importantly, an asteroid or two fused to its surface along with a massive, radiation-bleeding drive core somehow bolted on one end.

"Right ladz! Now we'z got da flashiest Black Kosmos Fing in da 'ooniverse! 'ERE WE GO! 'ERE WE GO! 'ERE WE GO!"

Four months later...

A massive impact crater is discovered on the barren world of Xaran IV along with the remains of a crashed Ork spacehulk. Like many spacehulks, the scattered wreckage includes some curious xenotechnology which the Adeptus Mechanicus may be eager to look at...

[Uraniun235]

That would actually be interesting - and frightening - if the Monolith were able to 'uplift' Orks. Intelligence to match their cunning? Yikes.

[The Yosemite Bear]

I still think the B5 response would be interesting, all the younger races getting uplifted, while the Vorlons and the Shadows got pissy...

[Kuroji]

nBSG Colonials: Kara and Lee make out behind it and nearly get naked until one of them comes up with some contrived excuse, and then they both go back to Galactica and sulk for the rest of the episode. Admiral Adama tries to blow it up to keep the Cylons from getting their hands on it after the president realizes that it's somewhere in the Sacred Scrolls and it's part of the grand roadmap to Earth, but some plot contrivance requires the fleet to jump out before they can actually hit it with any weapons.
nBSG Cylons: Xena, Warrior Princess... er, that is, D'Anna Biers, stares at it for a while before she, Baltar, and Caprica Six have a threesome on it. Cavil has her boxed after she realizes that it has helped her figure out who the Final Five are, and everyone gets back on the baseship and jumps after Galactica.

Neither group mentions it again. EVER.

[Night_stalker]

If the Necrons get it, the entire universe is now doomed. Naturally, the Eldar forsaw this and have placed a weapon capable of disabling it on a old Exodite
world, which is now a Imperial world.

[NecronLord]

If the Necrons get it, the entire universe is now doomed.

Why? There's nothing it can do (apart from lighting up gas giants, and I'd not put that beyond them) that they cannot.

[Ugolino]

Necrons:

C'tan are slightly amused by similarities between it and their pawns' architecture. Then destroy it, because it's a potential problem and they don't really need it.

[andrewgpaul]

There's already a Monolith in the 40K universe; the Ymga Monolith, near Tau space. As yet, nobody's done anything with it.