spirosd said:
I have a attached a picture of the circuit.
It's hard to tell how it's wired from a picture of a breadboard, but that looks really horrid!.
I'm presuming the device to the left is a 5V regulator, if so it hasn't got any capacitors round it, so it's very likely to be oscillating.
Secondly, the crystal and two capacitors should be as close as possible to the PIC pins - you've got them pretty well as far away as possible!.
If you visit my tutorials, I have a veroboard design for a 16F877 processor board - breadboard isn't really very suitable for designs like this. All the boards in the tutorials are actual practical boards, and have been tested with the code supplied - as already suggested, I also give advice on using the 877 instead of the 628.
As also has been suggested, it's really difficult to kill a PIC - I've put them in the wrong way round before, and burnt my fingers on them, but haven't managed to kill one (yet!).
But follow my tutorials, use a small 9V battery as a power source (not a multi-amp mains PSU), and you shouldn't destroy many components (or any!).