The ending of Shrek (2001) breaks Fiona's curse with a kiss, but she stays in her ogre form and accepts it as her true self.
Here is the sequence. Shrek bursts into the wedding on the dragon's back, tells Fiona how he feels, and Farquaad orders his guards to seize them. At sunset Fiona turns into an ogress in front of everyone. The dragon then eats Farquaad, so the threat to the swamp is gone. Shrek and Fiona kiss, and the curse breaks, leaving her in her true ogre form.
In my opinion the film's smartest choice is to refuse the usual reward. A conventional princess story would have restored her to human beauty, and Shrek instead lets the person Fiona hid all along be the one who is loved. This also resolves the earlier misunderstanding on the road home: Shrek overheard her call herself an ugly beast and assumed she was mocking him, and the ending shows her accepting the same shape he has.
The ending also closes the loops the opening set up. Farquaad sent fairy tale creatures to the swamp and offered the rescue deal so he could marry a princess and become king. The lava surrounded castle, the dragon that Donkey won over with kind words, and the wedding in Duloc all feed into the one moment where the dragon removes Farquaad. The party in the swamp, with fairy tale friends gathered around, fixes the problem that started the story too. The creatures Farquaad dumped on Shrek's land end up celebrating with him.
Shrek wanted to be alone, and he ends up with a settled household of Shrek, Fiona and Donkey. That group is the base for the rest of the series. By release order, Shrek 2 comes next, followed by Shrek the Third and Shrek Forever After, and each of them starts from a couple that already exists rather than building toward one. Chronologically the first film is only second in the series, because the spin-off Puss in Boots (2011) is set before it, so this ending is the first closing beat for Shrek himself even though it is not the earliest story in the timeline. If you are moving on to the sequel, see Shrek 2 next.