I hold an Indian passport and intend to travel to Europe to meet my German girlfriend and to travel with her a little within Europe. I have heard rumors that the invitation from a girl may result in a refusal of visa as the official might suspect me to be an illegal immigrant. I will be financing my entire trip, lasting 50 days.
Revealing in your application that you're in a long-distance relationship with a resident will make it harder for you to demonstrate that you have reason to leave the Schengen area at the end of the trip you have planned. The relationship will be seen as a reason for you to stay, and so you need to show proportionally stronger ties to your home country in order to convince the examining official the balance of your interests will be to leave. It does not automatically result in a rejection, though.
On the other hand, concealing this fact (which is eminently relevant to your travel plans) would be visa fraud, and that can have much more serious consequences than just having your application denied, if you're found out. So you should certainly declare her in field 31 of the application form.
Unless your girlfriend is providing a formal Verpflichtungserklärung, there's no need to enclose a formal invitation letter, copy of her passport, or that kind of thing. The focus is on establishing your conditions -- it's not as if being a citizen gives her any direct "vote" to influence the decisions of the civil service just on her say-so.