Ano Hi Mita Hana no Namae o Bokutachi wa Mada Shiranai/WMG

Yukiatsu murdered Menma, and now crossdresses as her in secret
If you look closely at the scene in episode 3 where Poppo sees what looks like Menma, you'll notice that not only is she slightly taller and her profile different, but that she's wearing the same watch as Yukiatsu. When Menma later reveals she was nowhere near there at the time, we cut straight to Yukiatsu looking at hair scrunchies for an unnamed party he refuses with a knowing smirk to reveal when asked. Later, when Poppo speculates that maybe Menma will get nostalgic and come back, immediately after Yukiatsu startles everyone by suddenly showing up. It seems likely that Menma's death (most likely at his hands) has left him seriously disturbed. In fact, I'll go one further and say that he's become so warped that he refuses to acknowledge his hand in her death, and likely blames everything on Jintan, his rival for Menma's affections, and will end up trying to murder him in a jealous rage, if not the entire group (Poppo will probably be the first to die, as he's seen too much without realizing it).

Menma's Wish is for Jintan to acknowledge his feelings for her
I may be off here, but that would make a whole lot of sense (despite it being really cheesy), considering that Menma died sometime after Jintan was put on the spot when asked if he liked her. Menma was obviously hurt when Jintan denied having feelings for her in a quite jerk-assy way ("Who would like that ugly...")

Menma's wish is to know the name of the flower they saw that day.
Hey, it could happen.
 * A variation on this: maybe Menma wants that flower that they saw that day. It could be a hard to get flower that Jinta promised to give her.

Menma's Ancestor is Viktor Reznov, and Ano Hana is set in the same universe as Modern Warfare series
And someone has to said that....

Her mother is Russian, and it could be she migrated to Japan due critical issues because of the Second Russian Civil War.

Menma really is a stress-induced hallucination
Think about it. Jintan hasn't only lost Menma, he lost his mom too. That kind of stress would trigger some pretty serious problems in a kid, not just being a hikikomori.
 * If we can take the story at face value, Menma is all but confirmed as real. She's able to influence the living world (anyone she touches notices the weight, etc.).
 * Not to mention Menma has information only she should know, specifically

Menma is really a stress-induced hallucination... But it's not Jintan's.
By a weird play of imagination and logic, Menma is really a hallucination by anyone other than Jintan but only he can see it.
 * Jossed.

Tsuruko was there when Menma died
Not suggesting that she murdered her, but she could have seen her die. It could also explain why
 * Most likely jossed.

Menma's wish will never be determined and wind up not mattering.
She was actually only there to help her friends get over her death, which is what really matters.

The "flower" is fireworks
We're on a fireworks plot thread in the show at the moment. It's worth noting that the Japanese word for "fireworks" literally translates to "flower-fire".

Jintan will die in the last episode
And that way, he'll join Menma and go to heaven with her.

Poppo watched Menma die
Somewhat self explanatory. The way he said that "all he could do is watch" and got really emotional about it.

Yukiatsu will commit suicide
"Let's go to heaven, Menma..."
 * Jossed.

The flower is Menma
The name Meiko means "A bud".
 * Those flower motifs in the OP and ED? Forget-me-nots, which just make the entire series so much more meaningful.