Speculah:Magical Powers
Abilities demonstrated by magical girls fall broadly into two different classes -- material magic, which involves the materialization of magical implements or the stylized transfiguration and reinforcement of existing objects, frequently employing the Soul Gem as a medium for the magical effect; and support magic, an umbrella category under which all other abilities are placed, influenced generally by the parameters of a magical girl's wish. Please note that this distinction is arbitrary and fan-made; canonically, no such categorization is applied.
Material Magic
This one allows to create or transform objects using a gem's power. We have seen many applications of this magic already - the magical girl costumes, all the weapons they create and possibly Kyouko's food as well. Sayaka's bat and the binoculars Kyouko used are examples of a enchantment/transformation of a mundane item.
Bind/Barrier
This one was a specialty of Mami's. She enchants Sayaka's bat so that it automatically protects her, and can be planted in the ground for a more permanent barrier. Energy ribbons are used twice - first to catch the suicidal lady and the second time to protect Madoka. She uses plantlike tendrils to bind Gertrud and lift Charlotte. Her ribbons with a chain-motif and a lock bind Homura and presumably seal her powers. Also, Mami's last "Tiro Finale" appeared to be a binding variant of the direct damage move she used previously. Mami's proficiency in this area leaves a question - what kind of wish could affect it so much? "I wish I fastened my seatbelt" is hardly a correct answer.
Support Magic
This one consists of few skills every girl can use, but the power of each skill heavily depends on their wish.
Healing
We see Mami and Sayaka using it. Mami used it outside battle and took some time to heal minor wounds on Kyuubey, while Sayaka used it in battle to fully recover from major damage Kyouko inflicted. Sayaka's power is explained by Kyuubey - her wish gave her very strong regenerative abilities. It is currently unknown if Mami's ability was a result of her wish or not.
Kyubey himself claimed that it was possible for every magical girl to fight even if every drop of blood was drained from their body due to the fact their bodies are just meat puppets they can repair with their magic. Sayaka simply seems more proficient at it, to the point that she can cut off pain completely.
=Timestop
Homura is confirmed to be able to either move faster than time or stop time. She can bring people into the freeze with her if she is touching them (possibly this only works with hand contact, as demonstrated by the fact she was able to move Sayaka away from Kyouko's attack without Sayaka realizing what happened, meaning Homura would have dragged her by the clothes or some other method).
This type of magic is granted to her by the fact her wish was related to time.
Due to the way stopping time works, it can give the impression Homura is able to teleport/blink around, when in fact she's just moving while time is stopped.
Object Creation
Demonstrated by Sayaka and Mami, and Kyouko a little bit as well. Magical girls seem to be able to produce an unlimited amount of their favorite weapons (rifles for Mami, swords for Sayaka, spears for Kyouko). They can produce them directly from their Soul Gem (as demonstrated by Kyouko) or from their clothes/hammerspace, as demonstrated by the others. They can also modify these weapons, such as making a large pistol for Mami or gigantic spears for Kyouko.
A sub-application of this power may be hammerspace, such as Homura storing firearms in her shield.
Another sub-application would appear to be the ability to imbue items with power, such as when Mami turned a regular baseball bat into a more regal looking mace of solid steel that could sprout spikes.
Barriers/Binding
So far we've seen that both Kyouko and Mami are able to generate barriers/fences to protect people (usually Madoka) or to keep them out of battles. Mami particularily seemed to specialize in this, able to turn her ribbons into intricate shapes and ropes or to produce strong ones around targets. Homura seems to have the ability to make magical shields to block attacks as well.
Telepathy
At least with Kyubey. We know he can communicate with magical girls telepathically and they can talk back to him, and possible to other nearby magical girls as well.
Time stop/Time bubble (unconfirmed)
Seen twice in ep.5. First, Sayaka uses it for few seconds to stop Kyouko's spear with a sword (that's first time we see water drops hanging in the air). Then Homura uses greatly advanced version of it - she leaves message to Madoka and then saves Sayaka, also giving her some time to rest (note how Sayaka is laying when Kyouko is about to strike, and how she's resting behind after Kyouko lands). Although full time stop does leave some major inconsistencies (Homura could use it while hunting Kyuubey and escaping Mami's bind), Time bubble (where time keeps flowing not personally for caster, but in some area of simple form, which can't be left without resuming time) explains most things. Is Homura is really proficient in this, it makes her wish heavily related to time, which supports the time loop theory.
Teleport/Blink (unconfirmed)
Alternate vision of Homura's skill. Time manipulation version does not explain Homura's appearing out of nowhere after being hit by a building in the prologue as well as some of her movements during the Charlotte fight. She might have both abilities, which leads to even more powerful wish and may have been foreshadowed by Sayaka's quip in Ep.1. Re. Homura and Madoka: "You're friends, meeting each other again after having traveled through space and time!"
Spatial Reconstruction (unconfirmed)
Referred to as Spatial Reconstruction Magic (空間再構成魔法 Kūkan Sai-kōsei Mahō) by Asian fans. In plain language, a user of this class of magic temporarily becomes the 'goddess' of a limited domain of space, gaining the ability to change, create, or destroy objects within it -- including distances and spatial coordinates. Humans appear to be shielded from manipulation to a degree, though their position may still be freely rearranged. Distinct from the 'object modification' described in the Material Magic section above -- where the qualities of an existing tool or implement are reinforced as it temporarily undergoes a highly stylized transformation -- inanimates affected by Spatial Reconstruction experience a permanent, unstylized alteration.
Speculah regarding Spatial Reconstruction began to surface after Homura intervened in the confrontation between Sayaka and Kyouko in Episode 5: Viewer discussion concluded that the complete redrawing of the wall layout, the floor, and the lighting in the background art following Homura's use of 'teleportation' was suspiciously unnecessary -- it would have been far easier for the animation staff to reuse previously completed artwork. If this was not in fact a production error, the theory followed that the ability used by Homura to save Sayaka may have been something on the order of reconstructing the space within the corridor, rather than mere teleportation or the use of a 'Time Bubble.' It should be noted that the alteration of the wall is presented unchanged in the scene recap at the beginning of Episode 6.
Outside the context of theory, Witches and their Familiars canonically employ magic within the spectrum of Spatial Reconstruction in the manifestation of their Labyrinths. Movement subjectively experienced by persons drawn into a Witch's Labyrinth does not necessarily indicate or overlap any analogous travel within 'real' space; observed space within a Witch's domain comprises thus of 'spoofed coordinates.' Ergo, the manipulation of the position or lay of objects in a given space figures fundamentally into the magical repertoire of a typical Witch. The 'cartoonization' attack used by H.N. Elly and her Familiars against Madoka may classify an offense implementation of Spatial Reconstruction.