RWBY/WMG

Ruby and Yang are missing a parent.
Initially suggested by the gravestone seen in both the "Red" trailer and the opening credits. And by the first line of "Red Like Roses", the song from the "Red" trailer:

"Red like roses fills my dreams and brings me to the place you rest..."

"Red Like Roses Part 2" (heard under the battle in V1E8) is even more explicit:

"I couldn't take it, couldn't stand another minute; Couldn't bear another day without you in it. ''All of the joy that I had known for all my life Was stripped away from me the minute that you died."

Yang mentions their father at one point, and uses the present tense. The only other relative of theirs that we hear of (as of the end of the first volume of the first season) is "Uncle Crow", and we don't hear much. What Ruby says, though, suggests someone at least in loco parentis for the younger of the sisters, if not an actual guardian.

Blake's bow is hiding animal ears of some sort.
This speculation dates back to the first appearance of her silhouette at the end of the "Red" trailer, which caused much debate as to whether the shape seen was a bow or ears.

The train Blake and "Adam" attacked in the "Black" trailer belonged to Weiss Schnee or her family.
Based on the presence of the distinctive "snowflake" logo on the crates and containers therein.

"Adam" is a faunus.
Initially suggested by Blake's apparent origins in Beauty and The Beast along with the third line of "Red Like Roses"

"Black the beast descends from shadows"

and the entirety of the "Black" trailer's song, "From Shadows".

Ruby and Yang are faunus, or descended from/related to a faunus
Ruby's "Uncle Crow" is described by Professor Ozpin as "an old crow". The usage is odd, but taken one way it may mean that Ruby's uncle is an avian Faunus. If he's a blood relation, neither married into the family nor a friend-of-the-family pseudo-"uncle", it may mean Ruby and Yang have some kind of Faunus heritage even if they show no signs of it. On the other hand, all the Faunus we've seen so far have been mammalian Half-Human Hybrids -- there's no evidence that there are non-mammalian Faunus.

Ozpin was on a team with Ruby's mother, and something went horribly wrong, leading to her death.
This is based on his unfinished line "I've made more mistakes than..." and commenting on Ruby's silver eyes, which he did as if recognizing them.

The lyrics of "Red Like Roses Part 2" also suggest that someone close to Ruby -- possibly her mother -- was a Huntsman or Huntress:

"I know you didn't plan this; You tried to do what's right. But in the middle of this madness, I'm the one you left to win this fight."

If true, it adds some support, however indirect, to this supposition.

Glynda and Cinder know each other.
When Cinder steps into the door in episode 1, Glynda's eyes narrow before Cinder's powers light up. Recognition?

Tying into above, the image of Ozpin, Glynda, Cinder, and Ruby's mother (Summer Rose is the current fan name, from the tombstone) being a Beacon team, with aforementioned screwup leading to Summer's death and Cinder's Start of Darkness.

Cinder is Blake's mother
Speculation based on the similar complexion, eyes, and dark hair.

Cinder is Yang's mother
An alternative, based on the fire powers in common. In this case, Yang was actually adopted into Ruby's family, not the other way around.

Cinder is the current ("new") leader of the White Fang.
During Blake's background montage, she never uses a gender-based pronoun to describe the new leader. This is to disguise that it's a she, and namely Cinder. Given Blake's backstory has her note "you could say I was born into it", it's entirely possible this ties back to the "Cinder = Blake's mom" theory and explains her defensiveness about the White Fang.

The White Fang killed Weiss' mother
Weiss' comments about the White Fang attacking her family's company are leaving out other details. She mentions her father a lot, but nothing about her mother. Her mother was another casualty, possibly so young that Weiss doesn't remember her much.

Weiss' father is abusive
Extending on this, Weiss's anger at the White Fang and the faunus is also a case of aiming her anger elsewhere than where it's deserved. She mentions her father came home furious every day, and her hand curls into a fist when she mentions a "very awkward childhood". It's possible that Mr. Schnee was actually abusive, and Weiss is directing some of that anger onto the White Fang and the faunus, rather than blame him.