Breath of Fire/WMG

Breath of Fire is the far distant future of the Pokegirls universe.

 * It would explain where all the animal folk came from.

Alternatively, Breath of Fire is set in the same world as Tellius.
Since we know there's more in the world than Tellius, but aren't sure what. The various tribes are different groups of laguz, though many of them seem to have lost or be losing their transformation abilities.

Or the same world as Tengen Toppa Gurren Lagann.
The world of Breath of Fire shares its population of weirdly ultra-anthropomorphized creatures with the Beastmen of TTGL - not to mention Dragon Quarter, set in a far, far future when and must excavate constantly to survive.
 * These need not be mutually exclusive, especially as per Word of God Dragon Quarter is in its own Alternate Universe.
 * There's also been a lot of speculation as to just how much Dragon Quarter in particular influenced the writers of Tengen Toppa Gurren Lagann, so (as with all Wild Mass Guessing) your mileage may vary.

Whilst we're engaging in Wild Mass Guessing about relationships between Breath of Fire and other universes, IV may be in the same world as Utawarerumono.
Not only do you have the kemonomimi running rampant (and in the artbook for IV it even states the Endless chose specific tribes of humans and changed them into furries to begin with), but you have two folks who are part of a split god. One of whom is involved with the Evil Empire and the other of whom is an amnesiac.
 * And the similarity of Japanese titles.
 * And the fact that both IV and Utawarerumono play very heavily from mythology of cultures that Japanese have tended to be very racist towards (Korean in the case of IV, Ainu in the case of Utawarerumono).
 * There's actually a rather strong possibility the writers of Utawarerumono may have been at least a little influenced by IV--Utawarerumono originally came out as a visual novel series in 2002, and IV was released in Japan in 2000.

IV could be in the same universe as Avatar: The Last Airbender, for that matter.
Let's review the similarities: Evil Empire in the west who wants to destroy the protagonist, Last of His Kind Crystal Dragon Buddha sealed away for hundreds of years, set in a Fantasy Counterpart Culture version of the Japan/China/Korea general area, and a bunch of chosen ones who are linked to specific elements who end up helping out the Crystal Dragon Buddha.
 * Of course those two bits of Wild Mass Guessing above only really work if you consider IV an Alternate Universe, though.

Myria is the result of Yuna's experiments on making gods being a success.
VERY popular Fanon for folks who take the "Breath of Fire IV is a Non Linear Sequel and in fact a prequel to I-III" interpretation.
 * At least one variant even posits that Myria is actually Elina who really did get turned into an Eldritch Abomination (and whose being turned into an "artificial Endless" was such a success that even the Dragonslayer couldn't permanently kill her).

Alternatively, Dragon Quarter is what happened after Yuna learned to make his own dragons.
At this point, this bit of Wild Mass Guessing is pretty much officially Fanon (as Capcom has issued its Word of God that Dragon Quarter isn't connected to the rest of the series) but it does occasionally still turn up as a theory.

Theories as to where, or even if, Breath of Fire IV fits properly in the timeline.
Yes, it's all pretty much WMG here. Blame Capcom for not giving us really anything to work with other than in the artbooks.
 * One of the more fan-preferred timelines is IV-I-II-III.
 * Others have suggested I-II-III-IV.
 * A very plausible argument exists in this troper's opinion for IV, like Dragon Quarter, being in its own Alternate Universe; the stories of how the gods came and chose people, and particularly some stuff re the Wyndians, doesn't match up neatly with the rest of the timeline. (For one, in I Wyndians were strong fliers and progressively lost flight up to III; in IV, Wyndians can hover but are poor in controlled flight, and are actually implied in the artbook to have been much stronger fliers but having lost some of their flight ability over time.)

Whilst getting into some REALLY wild mass guessing--possibly IV is its own universe but settled from folks from another world--even potentially from I.
The artbook for IV actually quite explicitly states that the only truly native sentient race in that world is the PabPab (who are also the sole race who were never chosen by an Endless). It's implied that literally everyone else was brought from or came from elsewhere and the Endless "adopted" them.

The birth of Deathevan resulted in Myria losing her destructive aspect.
This would account for the change in Myria's actions and motives between I, where she's a impulsive trickster god, and III, where she is a controlling mother god. This also ties neatly into my next Wild Mass Guess...

Deathevan is the source of the Desert of Death.
Still buried deep beneath the Earth, Deathevan is unable to assume material form, but he still drains the life from the surface world. Thus, you end up with two aspects of the same divine being at cross-purposes to one another, without either ever realizing it.

The REAL reason Capcom has shown a definite lack of Parental Favoritism towards the Breath of Fire franchise...
Capcom has had a long history of not really knowing what the hell to do with the Breath of Fire games in general (hence why it was such a shock when four phone games and a Comic Book Adaptation came out); most notably, it is probably the sole remaining Capcom franchise that has not yet been featured in a Capcom vs. Whatever game. Nobody really knows why. There is also a minor constellation of Wild Mass Guessing as to why the franchise has been in Development Hell for (at this date) nearly seven years:
 * One urban legend (inspired by Squaresoft's translation of I) is that the first Breath of Fire was actually a Square game that Capcom bought the rights for and the entire franchise is under some considerable restriction on its promotion/development as a result. (This is easily disprovable by the Japanese release being all Capcom's baby; Fan Translation from the original Japanese game has been very helpful in this regard.)
 * More plausible is the idea that there may be residual licensing issues from the North American release of the first Breath of Fire that essentially prevent the franchise from being included in a Capcom vs. Whatever. Square and Capcom actually share distribution rights in the US for the first game (due to Capcom having farmed out the localisation of I to Squaresoft) and this explanation does become slightly more plausible with the news SquareEnix is apparently working on ports of I and II to the XBox360 to be formally announced at E3. (Of note, Square Enix doesn't have distro rights for II unless Capcom is specifically licensing it.)
 * However, this technically wouldn't prevent any cameos from III-Dragon Quarter unless there's other licensing issues we don't know about...
 * Another urban legend states that the creators of the series essentially prohibited Capcom from including the series in any Capcom vs. Whatever games.
 * And pretty much each and every single Urban Legend of Zelda regarding why the Breath of Fire franchise has never ended up in a Capcom vs. Whatever got blown out of the water by a recent tweet from the Marvel vs. Capcom development team (which in and of itself has, in addition to the CEO of Capcom leaving, added considerable fuel to the "are they going to revive Breath of Fire" rumour mill).
 * Specifically, there were plans to add Fou-lu from IV as a playable character in Marvel vs. Capcom 3--plans that got nixed as the Marvel vs. Capcom franchise was marketed primarily for Western audiences and Breath of Fire was seen as less popular in the West. The same development team has expressed interest in having Fou-lu in a future Capcom vs. Whatever--so at least for IV, there's no problems with licensing that would prohibit a Capcom vs. Whatever.
 * Another urban legend is that Capcom was trying to sell the franchise to another company, but this was largely disproven when Camelot Games actually tried to buy the rights to Breath of Fire (Capcom refused).
 * One urban legend (which is in part responsible for the Broken Base regarding Dragon Quarter) is that Capcom was so disappointed in international sales of Dragon Quarter (despite being a best-seller in Japan and even for a week in the US) that they pretty much have put a semi-permanent freeze on further games in the franchise or even references to the franchise's existence.
 * This is partially proven and partially disproven; there hasn't been an official announcement of a new Breath of Fire, and there was (comparatively speaking) very little Expanded Universe material ever made for Dragon Quarter other than the artbook and the soundtrack. It is known from the developer's blog by the creators of Dragon Quarter (now offline) that the creators would have liked to do a Breath of Fire VI using the same game engine as Dragon Quarter--if this was the case, this was probably rapidly shelved when Capcom saw just how much of a Broken Base had developed (there are still some who refuse to recognise Dragon Quarter as even being in the franchise).
 * In other words, the official policy of Capcom is not only to deny that Dragon Quarter ever happened but to deny that the Breath of Fire franchise as a whole happened, at least outside of Japan.
 * However, there has been a lot of promotion of its immediate predecessor Breath of Fire IV in Japan (and more recently, in France and China), especially since 2007 (when both three separate Japanese smartphone games--two of which can be considered a Non Linear Sequel to IV itself--and the Comic Book Adaptation of IV were released); this has led to Wild Mass Guessing on its own that Capcom is probing interest in a Breath of Fire VI that is either a sequel or prequel to IV.
 * At least some media reports have indicated that developers at Capcom have a real interest in reviving the franchise (which has actually been backed up by the jettisoned Marvel vs. Capcom plans) but that the main issue--per the CEO of Capcom at the time--was funding. (The CEO who gave the statement resigned from Capcom effective November 2010, which has in and of itself revived rumours that the series may finally exit its seven years of Development Hell--the popular perception has been that the CEO (who was responsible for the Mega Man franchise) may have been nixing revivals.)
 * One bit of circumstantial evidence that does give some credence to the "former CEO put the kibosh on any new Breath of Fire" idea--said CEO was also the primary developer behind the Mega Man Legends series; almost all the RPG spinoffs have become a bit of The Unfavourite since he has left Capcom (almost to the degree that the Breath of Fire series has suffered), and the company is actually acknowledging Breath of Fire enough to have re-releases (on PSN) and in multiple "card game power-up" cameos in Ultimate Marvel Vs. Capcom 3 (in what is, by far, probably the most high profile any Breath of Fire character has been in a Capcom vs. Whatever yet).
 * At least one rumour posits that a major developer for the franchise has either died or left Capcom. No reason why it wouldn't stop development, though...