Because of how she dresses in the Windows Touhou Games, her exposed armpits are sometimes the target of jokes and memes, with "Waki Miko Reimu" or 「腋巫女霊夢」 being a popular phrase.
The drastic change in the color of Reimu's skin tone over the course of the Windows games (most noticeable in Mountain of Faith, in which her skin appears yellowish and almost jaundiced) raised eyebrows and led to a number of jokes and dubious theories, the most common of which is that she is actually an undead zombie.
Fans have noticed that Reimu has canonically yet to be defeated in battle, due to the fact defeating her will possibly cause the Hakurei Border to collapse. Thus, her personality has received a bit of negative reception due to this.
Reimu has never been seen to get any donations at the Hakurei Shrine. This causes fans to make jokes about her never getting donations.
In Embodiment of Scarlet Devil, it has been said that pretty much nobody goes to the shrine. Thus, it has been a common interpretation that she gets 0 donations. Due to this, she is called 貧乏巫女 (Binbou miko, lit. "destitute shrine maiden").
A defeated Reimu is sometimes called "Taoreimu" (from 倒れる), a hit Reimu is sometimes called "Dareimu" (from 打), and an angry Reimu is sometimes called "Buchigireimu (from ぶち切れる), thus giving her shiritori-like names.
Sora No Amagumo has made a comic series most centered around Reimu with a few major changes: She's a silent, kind adorable girl, a contrast from the more common surly Reimus out there. And this rendition is pretty popular on both parts of the fandom.
Some fans theorize that Reimu IS her shrine's god, but she is either oblivious to it or keeps it a secret. However, this would also mean that the Hakurei's before her were the shrine's gods as well.
Due to the fact that she never gets shrine donations, some fans had her personality being greedy to money, and takes whatever she can to get it, some fan comics even showed that throwing a coin at the opposite side of Reimu is enough to distract her for a period of time.
Her face in the bad ending of SoEW has become a popular meme recently.