Phineas and Ferb has a lot of stories where Perry somehow becomes a human, and oh, it also turns out he and Dr. Doofenshmirtz are both gay. Often Dr. D is the one who transforms him in the first place, though usually for ostensibly different reasons.
It's common to speculate about the boys' respective missing biological parents. This contains a whole subgenre where Doofenshmirtz turns out to be Phineas's father, with various back stories trying to fit this into canon. This is, of course, greatly helped by the reveal that Doof and Linda actually did go on at least one date when they were younger.
Building on this, it is also very common practice to make Ferb's biological mother abusive, as an explanation for his quiet and reserved attitude.
Conversely, it's become somewhat popular to make Phineas and Candace's biological father a Jerkass to some degree; this is mainly so the author can have a scene where the man shows his true colors (often after kidnapping Phineas) and Phineas takes it badly.
A lot of fanfics put the kids in school. Since the creators have stated that the series will only cover time off from school, there seems to be a general fandom curiosity as to what school is like for the characters.
Similarly, a very popular plot in fanfics is aging the characters into high-school, and sometimes further than that into adulthood.
At the end of Phineas and Ferb The Movie: Across the 2nd DimensionIsabella kisses Phineas on the lips just before they're hit with an amnesia ray. This has become a convenient plot device for a lot of ship fic writers. The most common variation is that Phineas or/and Isabella remembers the kiss somehow (very often, the memory returns to them in a dream), and decides to act on it. Another variation is that Phineas gets Carl to stop long enough for him or Isabella to write down a message to themselves.
Fanfics about everyone's memory getting returned are equally common.
It is quite common for some fanfics to show characters actually being related that might not actually be related in the show (such as Stacy Hirano and the Fireside Girl Ginger, though this one has since becomeAscended Fanon).
One popular topic is the day that Isabella first meets and/or gets her crush on Phineas.
An increasing trend is to put the Fireside Girls (either individually or as a group) as the main character/s. This is mostly due to the present rumors of a Fireside Girls spin-off show.
The Meap Me in St. Louis story that the creators have no plans to create.