German Slugs properly transliterates umlauts and the letter ß appearing in titles for slugs (i.e. for pretty permalinks).
While creating a post or page, WordPress automatically suggests a permalink. If your permalink structure contains the %postname% tag, then the title of your post or page will be used, simplified by conversion to lowercase, replacing spaces with hyphens, removing certain punctuation characters and removing diacritics from latin letters.
Thus, by default, ä is replaced with a, ö with o, ü with u and ß with s (similar for capital letters). For German, the conventional transliteration is ä to ae, ö to oe, ü to ue and ß to ss (sometimes sz in Austria, this is not yet supported). This plugin makes your WordPress apply the conventional transliteration.
I wrote this plugin because manually correcting WordPress's suggestions is a considerable hassle, especially if you decide to change the title afterwards.