I think the base capacitor is not needed. The diode in parallel to the relay coils are very IMPORTANT though.
If absent, the NPN transistor will be damaged due to reverse voltage generated by the coil after it is de-energized.
If you are using multiple relays in your circuit, you could use ULN2003 as relay drivers.
This is multiple darlington transistors in one 16 pin DIP package including the resistors and diode.
Easy interfacing for beginners