Rather an important part of your motorcycle, those black bands of rubber keep you going, stopping and turning. Scroll down for some articles on tyres in relation to the Honda CX and GL V-twins.
There are plenty of tyres out there to choose from; what do you need to look for?
Pirelli Sport Demons (in 100/90-19 front and 110/90-18 rear) seem to be popular in the CX community, as do Michelin Commander II tyres.
Tyres should be discarded once they reach a certain age - see this article on tyre age.