If you find your download speeds are decreasing, it's worth turning the router of for 30 secs or so. This will (if you're on ADSL) kick the speeds up again (usually). Apart from that, I leave mine on all the time.
I switch mine on when I power up the pc and switch it off when I shut down the pc. Up to you as to whether you waste a miniscule amount of electricity. Does not appear to have any undue effect on my router or connection. Been doing this for over 4 years now.
With a previous ISP (ZEN), I found that switching it off everyday caused my line to resync at a lower level, for example, it would be syncing at 8128kbps, after the overnight switch off it would resync at 6500kbps, not a bit amount but it could take up to a few days to resync back to 8128.