How to respond to a citation request which is not relevant? Often, as soon as I submit a pre-submission paper on the arxiv, I receive a couple of emails from other researchers pointing out their previous relevant work, which in their words is connected with mine and deserve citations. 

Sometimes, it happens that their work is really connected with my work, and perhaps even anticipating it. For some reason I was not aware of that, my fault. In these cases, I usually add the citation and even refer to the work in a more extensive way. 

However, most of the emails just point to works that are indeed on the same topic, perhaps also very important works in the field, but which are not even similar nor related to my work. In this cases, I really don't know what to do. 
I could inflate the reference of the paper, giving credits to papers which really did not contribute in any way to my work. Or I could just ignore it, with the hope that one of the authors of that papers will not end up to be one of my referees...

What is the common practice in this cases?

(see also this question for another point of view)
Opinions vary, but I think it is very important to acknowledge prior art, that is, priority. To leave important prior (strongly related) work out of a bibliography is to communicate the idea that there was no prior work. Indeed, one can "cultivate" lack of references to one's competitors by carefully not looking at their work, thus, seemingly having no obligation to cite them (or otherwise acknowledge their existence!?!) But this is inappropriate, as it would convey a false impression to your readers, as well as being unfair to your competitors or predecessors. That is, it's not only what you use or rely on, but works that came before yours.