As in, I know that all Droids have the micro USB charging connector. But what if I used a charger of HTC make, or for that matter of fact a charger of RIM (BlackBerry) make, to charge my Android phone (which is not of aforementioned brands) to charge my phone? Will this cause (short/long term) harm to my battery? If so, why and how?
No, it should be fine as long as the charger is meant for a cell phone.
Most of the major cell phone manufacturers adhere to the the International Electrotechnical Commission's mobile phone charging specs which specifies the use of the micro USB charging standard. USB 1.0 and 2.0 is capable of delivering 0.5A at 5V and USB 3.0 is capable of 0.9A at 5V. Not all chargers adhere to those specs, but most phone chargers deliver a charge somewhere in that range. I have had several HTC, Samsung, Motorola and some off-brand phone chargers and they all are 5V and put out between 750mA and 1A.
Also, your cell phone has a charging control circuit and voltage protection circuit that protects the device from power outside its acceptable spec. I believe it also monitors temperature and will terminate charging if it falls outside of an acceptable spec, but I'm not sure about that.
Some tablets like the Nexus 7 come with chargers that put out 2.1A at 5V. Using this charger will charge your phone faster but it will also cause the battery to heat up more. Excess heat can degrade the life of a battery so I wouldn't make a habit of using a tablet charger on your phone.