Rinoa becomes a Sorceress partway through the game. Sorceresses in the world of Final Fantasy VIII are prone to becoming evil and wreaking terrible destruction; at the time of the game, the world is just recovering from a conflict known as the Sorceress War. Concerned, Rinoa goes to Edea Kramer, a former Sorceress herself, for advice. Edea explains that Sorceresses can easily become corrupted by their power, but that this can be avoided by relying on the support of friends. In particular, Edea advises Rinoa to find a Knight who can offer her emotional support. Rinoa's love interest, Squall Leonhart, volunteers to be her knight.
Based on this conversation, one theory suggests that the evil Sorceress Ultimecia is actually a future version of Rinoa, driven mad by grief after Squall's death, who intends to compress time as a way of regaining her beloved.
Others claim that Ultimecia is in fact a future Rinoa, based on several hints within the game such as the fact that Ultimecia's GF bears the same name (Griever) as a ring that Squall gives to Rinoa during the course of the game. However, before fighting Griever, Ultimecia claims to attach to one of the party members (Squall). It can be assumed that, in doing so, Ultimecia's GF or, in fact, Ultimecia herself takes a part of Squall which he holds close - the Griever emblem. As such, it should also be noted that Griever is not only part of the ring which Squall gave to Rinoa but is, also, presumably, the lion head at the end of his keychain and on part of his many belts.
In regards to the Rinoa/Ultimecia theory, however, it should be mentioned that the two share near identical facial structures in FMV sequences (which is emphasized by the final shot of Rinoa's face within the game, which flashes several times to Ultimecia's). Furthermore, Rinoa and Ultimecia are the only two Sorceresses who are shown to have wings--Rinoa grows white wings for her Angel Wing Limit Break, and Ultimecia possesses black wings when you meet her at her castle. Due to the Knight references throughout the game, it can be expounded that as her friends died around her, Rinoa became dark and twisted and yet Squall kept his promise to be beside her always. As such, he became Griever.
There is also a possibility that Sorceress Adel's powers--which were given to Rinoa upon Adel's death--may have carried some of Adel's evil with them, which perhaps began to corrupt Rinoa even before the game was over. Upon Squall's death, Rinoa, driven mad by grief, might have opened herself fully to the evil in the power she had inherited, and could have even become so possessed by the Sorceress Power that it recreated her body as a malleable structure of pure magic that could survive long enough to reach the time when it decided to call itself Ultimecia and eliminate all other matter.
This theory is attractive because it provides Ultimecia with the depth, background, and motivation that many felt she lacked, but the evidence supporting it is purely circumstantial. Some point out that if Ultimecia wanted to regain Squall, she probably wouldn't have tried to kill him.
Square has directly stated that Rinoa is definitely Ultimecia.