I lift weights twice/week during the off-season, once/week during the race season, except for the week before 'A' races when I'll usually skip the weights as part of my taper. I do complex barbell lifts like squats, overhead press, deadlifts, rows/chins, etc.
I think it helps on the bike. Not so much at threshold and higher intensities, where it's more about how much oxygen your cardiovascular system can deliver to the muscles. But at sub-threshold intensities some studies have shown that the additional strength gained from weight lifting makes your legs more fatigue-resistant. Basically my "all day pace" is at a higher power output than it would be if I wasn't lifting.
There are other benefits off the bike, especially as you get older. Losing bone density and muscle mass are common as people age, and strength training can prevent that. Cycling is not a load-bearing activity so it doesn't do any good for bone density and joint health.