Speculah:Make a Wish
Kyuubey's proposition includes granting a wish in exchange for the person to become a mahou shoujo. This page lists those who have encountered Kyuubey and guesses about wishes. Note that these are speculations and not the character's actual wishes.
Madoka's Wish
Deus Ex Machina or "I wish Mami were alive"
Madoka wishes Mami back to life. This one is so easily corrupted, especially if the "Witches are fallen magical girls" theory proves true. You wished her alive Madoka, you never said as a magical girl!
Fight to save people
Madoka wishes to help everyone in need, from suffering people, to the fallen such as Mami, to the witches lost in grief. She becomes a magical girl with the potential to solve any problem, but neither she, nor Kyubey, nor other magical girls have any idea how her powers work, so saving the world is still easier said than done.
Procrastinating Until the End of the World
Madoka resists making a wish until the very end of the series, when the apocalyptic scenario from her dream comes into play, and she uses her wish to solve everything at once or cause a global reset. "I wish everything would go back to the way it was before I met Kyubey!"
The Human Instrumentality Project
Madoka wishes to end all suffering. Everyone gets hugged and turns into Morning Rescue.
Homura's Wish
Do you really want her dream to come true?
Homura might have used her wish to help someone else (Madoka?) and is the person Mami was referring to when asking Sayaka whether she wanted to make someone's dream come true, or be thanked for making it come true.
If you do, you'll lose everything
Homura might have wished to become the perfect girl and undo her previously unhappy life. She was a classmate and friend of Madoka, which is why she knows her way around the school. However, everyone's memories of Homura vanished because she wanted her old flawed, bullied, unpopular self to be forgotten.
"Anywhere but here!"
Because Sayaka wished to heal Kamijou, she received healing powers in addition to the powers all other Magi have. Homura has a unique power as well - She can either teleport or move faster than the human eye can follow. This suggests that her wish had something to do with movement. One likely conclusion to draw from this line of reasoning is that she used her wish to run away from something, possibly an abusive family.
"I wish my Oneesan was an unstoppable magical girl!"
Rather than choosing to be a magical girl herself, she was wished into being a magical girl -- perhaps from someone who loved her, such as a little sister. The little sister, or someone similar (another member of the family? A friend?) specifically wishes that Homura would be unstoppable, and ends up becoming a magical girl alongside her, but then dies in battle later. Homura, however, has become "immortal". If this was so, this would make her the one Mami is talking about when she warns against making wishes for other people. It also explains why she doesn't die/become injured when Charlotte chomps on her, why Kyuubey seems to flipflop on his involvement in her wish, why Homura seems so mature (and claims to have seen many magical girls die in her lifetime), and why she doesn't appear to have any family (all of her family members have died from old age). (Original poster: The "immortality" bit of this might not apply since episode 6; every Puella Magi is effectively immortal if her soul gem is not destroyed. Not to mention this theory doesn't explain Homura's superspeed.)
Mami's Wish
"I don't want to die alone!"
Before she met Madoka and friends, Mami was all alone-- her apartment was empty except for her presence, and had no contact with her family. When Kyuubey made his offer, Mami wished to not die alone. As in many "deal with the devil" stories, the contract is upheld, yet in a twisted manner: Mami made new friends and immediately died before their eyes.
"Please help…"
In manga canon, her wish is shown to be simply "please help" after being questioned by Kyubey about her wish in a car accident.
Sayaka's Wish
Kamijou
As of episode four, Sayaka's wish has been confirmed; she has wished for Kamijou's arm to be healed. As a side-effect, the wish granted her the ability of fast recovering. Whether there are any downsides to this wish (such as the healing being temporary, Kamijou being killed shortly after his recovery, etc.) remains to be seen.
Kyouko's Wish
I want to eat
According to abandoned child theory, she once almost ended up starving to death and wished for food when Kyuubey appeared with his proposal. Since that time she does not have problems with hunger as long as she gets Grief seeds.
Someone believe my father
Revealed in episode 7 that, Kyouko wished people to believe in her father's unorthodox teachings.