I have a Raspberry Pi B+ hooked up to my router and I leave it on all of the time, it rarely gets switched off. Does this cause any damaging effects to the Raspberry Pi?
No, leaving the RPi on all the time won't harm it at all. The RPi is designed to be an embedded device, and run in an enclosed space. Unless you have it somewhere stupid like an active dryer vent, your device should be fine.
You are actually far more likely to damage the device by constantly unplugging it.
The only thing wearing out is the sd-card if you write to it (for instance log-files). There are lots of guides how to avoid write accesses. For instance you can mount /var/run,/var/log and /tmp in ramfs and tmpfs
a snipped from my fstab:
none /var/run ramfs size=5M,noatime 0 0 none /var/log tmpfs size=5M,noatime 0 0 none /tmp ramfs size=50M,noatime,mode=1777 0 0