This was touched on in another meta, but I think it deserves a more in-depth discussion. It's also something we should straightened out now, because the current usage of these tags are already getting a bit out of control.
As of now people just seem to be tossing the anime and manga tags onto a question based on whether they are reading the manga, or watching the anime. I don't see what purpose this serves, since the question will apply to both the manga and the anime, and the answers will often be the same. In the situations where they aren't users can indicate this in their answers, stating whether this answer applies to the anime or the manga (and, ideally, could answer for both). Having two separate, yet identical questions, one for the manga and another for the anime is just redundant (and messy).
There are some exceptions to the "small difference" of course, where the anime and manga are significantly different (The first Full Metal Alchemist (FMA) anime and Manga are a perfect example of this), but in these situations having a separate tag for the manga and the anime makes more sense (i.e. something like full-metal-alchemist and full-metal-alchemist-2003-anime). It's much easier for a user to only need to search one tag, rather than two, and it also allows users to ignore questions from one work and not the other. Continuing on my FMA example, if I've watched the anime but I haven't read the manga I'd want to be able to ignore all of the manga questions to avoid spoilers, but would still like to be able to see questions about the 2003 anime.
Furthermore, if they anime and manga are that different, then I'd consider them independent yet related bodies of work anyways, and thus both deserving of their own tag.
It also fails to be useful as a filter. Considering the entire site is about anime and manga, then every question is going to be relevant to either an anime or a manga. It would be akin to tagging questions with programming on Stack Overflow. Performing a searching with just programming isn't going to help, I'll always need to use another tag for it to be useful. The same applies to anime and manga with their currant usage.
My first thought would be to state that the manga and anime tags should only be used when it's specifically about topic of manga and/or anime, and not about a specific work. However, I feel like this needs to be fleshed out more through community discussion.
An example of the above usage would be What is the difference between doujinshi and manga? This isn't about a specific work, but manga as a whole. In this question the tag clearly indicate what the question is about: manga terminology.
When should we use the anime and manga tags?