Tier 1 - Mutually Canon (They definitely share a universe)

I'll be separating each property mentioned into tiers (hey I told you I put too much thought into this). This tier is for properties where characters from Animaniacs have shown up in them as themselves, and vice versa. These have to be more than just references. No parodies, knockoffs, cases where the characters exist but are fictional in universe (as in they're not toon actors, they're fictional cartoon characters with no thoughts of their own), etc. These are part of the ASU, no question.

Tiny Toon Adventures

First, there's the fact that Ralph debuted in Tiny Toon Adventures, before he became a recurring character in Animaniacs, although he was unnamed at the time:

Then, once Animaniacs started, characters from Tiny Toon Adventures would often make cameos, and Animaniacs characters would cameo in Tiny Toons' post-series specials:

Before I move on to the next property, although most of the properties mentioned in this post don't always adhere to continuity, I still only want to provide evidence from content that at least could be considered canon, so while I feel obliged to acknowledge the existence of "Pinky, Elmyra and the Brain", given that it isn't canon, it's depiction of how these characters share a universe doesn't really matter.

Pinky and the Brain

A pretty obvious pick, given that Pinky and the Brain were initially just Animaniacs co-stars before getting their own show:

Their spin off series has plenty of references to Pinky and the Brain's adventures in Animaniacs. Also, Phar Fignewton, Billie, and other Animaniacs characters all make appearances (with Billie and the Warners appearing multiple times):

Those in addition to the series finale ("Star Warners"), where the cast of Animaniacs reunite to do a sketch that parodies Star Wars, make it clear that the spin off definitely takes place in the same world as Animaniacs.

Freakazoid!

This show is more removed from Animaniacs than the previous two properties, but Wakko and Brain show up in Freakzaoid, and Freakazoid shows up in Animaniacs and Pinky and the Brain, so it's in the ASU alright.

Space Jam/Classic Looney Tunes

I realise that Looney Tunes in general doesn't really have a "universe", just various iterations/reboots. So the versions of the Looney Tunes I imagine exist in the ASU are the ones in the Space Jam movies/classic shorts (or pretty much any version of them that are toon actors in the modern world).

The Looney Tunes appear or are at least mentioned in Animaniacs multiple times:

Space Jam is alluded to in the Pinky and the Brain episode "Inherit the Wheeze", and the Warners are in Space Jam: A New Legacy (their water tower is even placed in Looney Tunes World in the movie).

There's also the fact that Tiny Toons is an official Looney Tunes spin off, so presumably if Animaniacs shares a universe with that show the Looney Tunes should therefore exist as toons in the ASU.

Tier 2 - Implied/Headcanon (They could share a universe)

For cases where Animaniacs or another ASU property implies that they share a universe, but this isn't done the other way round (for example, if a character from the property appeared in Animaniacs, but no characters from Animaniacs appear in their franchise). This can be done via references, cameos, mentions, etc., but they have to come off as more than just references/jokes, they have to imply characters from those properties really do exist. Basically, the Tooniverse may consider them canon, but the feeling isn't mutual (yet, at least).

Mickey Mouse & Friends

For this franchise, when I say they might "share a universe" it's assuming the context is that Mickey and Friends are also toon actors in the real world, like the Warners, Slappy, Bugs, etc. I'm also including Goof Troop stuff, Donald Duck universe stuff, etc. WB cartoons reference/take shots at Mickey/Disney ALOT, so I'll only talk about a few references that imply that Mickey, Minnie, etc. are real people in Animaniacs.

Slappy mentions attending Daisy Duck’s bar mitzvah in a season 3 segment called "Gimme a Break", so that implies Daisy, and therefore the rest of the gang, really do exist and aren't just fictional characters. She also mentions Huey, Dewey, Louie in the same episode. She mentions these characters while delirious, but one of her gimmicks is being reminded of younger versions of other cartoon stars she's met, so who's to say she hasn't actually met them?

Dot says "Why don't you go bug the kids on Goof Troop?" to a nanny in another season 3 segment called "The Sound of Warners". Again it's just a mention (and a sarcastic one at that), but it does imply that they are real people in their world.

DuckTales has been mentioned a few times; by Pinky in "Opportunity Knox" ("Egad, this is better than a DuckTales episode.") and Yakko mentions the DuckTales reboot in "Suspended Animation - Part 2".

These references alone don't imply Scrooge, the triplets, etc. are real, but alongside the previous references, it does seem to imply that the cast of DuckTales are animated actors in this world too (Animaniacs, the show, exists in-universe too yet the Warners are real people).

All these and more just seem to repeatedly hint that Mickey and his pals are toons in Animaniacs just like the Warners, but since they're from another studio we can't see them onscreen.

This is supported by the possible presence of…

Roger Rabbit

Ralph greets Roger as he enters the lot in the limo (presumably with Jessica) in Tiny Toon Adventures, and although we don't see Roger's face and he's wearing grey gloves rather than yellow ones, Ralph explicitly refers to him as "Roger":

He shows up again later:

OK I admit this one's kind of a cheat because this guy could count as a knockoff (different clothes), but think about it, if he is just supposed to be a knockoff, why hide his face? Why make sure we never see him up close? He's one of the only supposed knockoff characters they do this with. It just implies that this is actually supposed to be Roger, but for the sake of copyright they keep his face away from the camera, since Roger Rabbit is considered a Disney property.

Mickey, Minnie and more appear in WFRR, which goes perfectly with the implication that they are toon actors in Animaniacs. It’s also one of the only properties where both Bugs and Mickey exist (or in Animaniacs' case, Mickey is implied to exist) in the real world as themselves and not parodies or fictional characters. I'm just saying, Animaniacs and Who Framed Roger Rabbit being taking place in the same world would make sense, considering they are both about toons in the real world.

Plus, Steven Spielberg directed Who Framed Roger Rabbit and even voices the "knockoff". I think it's only fitting the movie that got him invested in directing animation shares a universe with the rest of his animated work.

Tier 3 - Reaches/Outside References (It's possible they share a universe, but unlikely)

For cases where a property implies/shows that Animaniacs/ASU characters exist in their world, but this has not happened the other way round. This tier is also for cases where the property has no canon and hence can't share a universe.

Histeria!

Some of the character models that were used in Histeria came from Animaniacs (like ones for caricatures of historical figures such as Michelangelo and Ludwig von Beethoven), and some Animaniacs characters are mentioned/seen in Histeria!:

So why isn't it in Tier 1?

Two reasons. First, in regards to the character models, this seems to be a case where they just reused background character designs rather than intentionally putting an established character in a different show. For example, the World's Oldest Woman was not given a name until Histeria! and was slightly redesigned, and Ludwig von Beethoven has a different voice in Histeria!, so they're not really official appearances of those characters as their Histeria! selves. Yes that's a similar situation to Ralph, but the difference is that the background characters have completely different roles in Histeria! whereas Ralph is the WB security guard in both Tiny Toons and Animaniacs and looks exactly the same (Frank Welker even voices him in both). In the case of the historical figures, two properties depicting the same historical figure does not mean that they share a universe.

As for the Animaniacs references, Histeria has no canon. It's not like Looney Tunes and Space Jam where there's at least a duology of films where one continues the story of the other. There are recurring characters and gags but each episode is completely standalone (different settings, time periods, etc.), unlike most of the other properties which are episodic, but do have continuity (Miss Flamiel is hired in her debut episode and continues to be the Warner's teacher in later episodes, Snowball buys Microsponge in season 1 of PATB and still owns it in season 4, etc.) Histeria! exists in it's own little reality-warping world. Therefore any references to Animaniacs are just that: references.

Teen Titans Go!

Yes, really.

Starfire mentions that the WB water tower is where "the Animaniacs" live in "Teen Titans GO! To the Movies".

(Yes they make the mistake of calling the Warners "the Animaniacs" when that name is meant to refer to the entire recurring cast of the show, but to be fair official Animaniacs media has made this same mistake so whatever.)

And before anyone thinks "Well she's an alien who probably doesn't understand that cartoon characters aren't real", TTG is yet another show where toons are actors in the real world. This is confirmed in multiple episodes, such as their Warner Bros. 100th Anniversary special:

So Starfire knew exactly what she was talking about. The thing is, the Warners themselves don't appear in any episodes of the show, neither inside or outside the water tower. However, the Animaniacs cast may still exist as toon actors in their world. This is implied by:

TTG'S ACTUAL CROSSSOVER WITH FREAKZOID. Granted, he is sort of treated as a fictional character, but in a meta way that would fit right at home in an episode of Freakazoid. The toon actor reasoning can still apply. The point is he's interacting with the real world and doesn't only exist within a TV screen. However, until TTG itself is referenced in some way in either official Animaniacs media or some other ASU property, these are just references.

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I realise most of these were probably just seen as fun cameos and/or references and nothing more, but the idea of the Warners and Bugs Bunny canonically being co-workers who have known each other for years, or something like Dip actually existing in their world, etc. just feels right. Helps the world seem...larger, and more developed! (Goodnight Everybody!)