It depends!!
Nearly every ADSL line will exhibit overnights drops in SNR. Some may only vary a small amount, but some may vary by a large amount.
Sometimes, this SNR change can cause a resync event. Too many of these can cause your speed profile to drop.
Of course, some ADSL lines will only suffer a small SNR drop overnight, and others will suffer a larger one so it is very dependant on your individual line conditions.
HOWEVER
During the training period, it is a "good thing" to teach your exchange about the quality of your line, so it is recommended that you reboot your equipment at least once or twice a day.
HOWEVER
Some lines, (particularly those at the extent of ADSL service) may actually suffer when you reboot the router, and the sync speed may actually creep up a little after a reboot as the exchange uses DLM to improve your conditions. For these types of lines, it is usually better to leave your router on for as long as possible, and to only restart them in the morning when external interference is at it's lowest.
HOWEVER
Some routers can actually 'clog up' with connections, (for example for those users who use P2P style applications). This can exhibit itself with symptoms such as slower and slower performance, through to a complete lack of connectivity with certain applications. Obviously, in these cases a reboot can be very useful!
HOWEVER
There is also the argument for saving power (although modern routers consume very little power). The old "turning off and on too much will blow it up eventually" argument has also been put forth. Also, some routers do get hot in operation, and it may give you peace of mind to turn it off when not in use. That being said, I've never come across a router that spontaneously combusted!
So really,
it very much depends on your personal line conditions as to whether it is desirable to keep your router on, or turn it off.One thing I will say, is that *frequent* reboots are a Very Bad Thing(tm). More than four or five resyncs in an hour is almost definitely going to make the DSLAM adjust your speed profile. Reboots in moderation
B.