Progressive resistance is a fantastic idea. It basically says that in order to get stronger just add a little weight to the bar each time you're in the gym. Add some weight, lift it, and your body adapts to the newer strength requirement by getting stronger. Fantastic! Keep adding a pound or two to the bar at each and every workout and everyone can have a 1,000 lb. bench press in, at most, 20 years.
We all know that as important as progressive resistance is, it just doesn't go on forever. You can't simply continually progress, at least not without some kind of artifiical enhancement. Instead, most trainees find that this system works great for a limited time - depending on the person - and then they stall.
Dan John said in his book that any program will work for about 6 weeks and no program will work for much longer than that. I don't think either Dan or I have any convincing scientific evidence to support that 6 week timeframe, but it seems about right. You should assume that the gains from your strength training program will fall off after 6 weeks or so and plan to overcome that. How? By changing your program.
What should you change? I'd suggest varying your exercises, equipment used, rep ranges, and volume every 6 weeks or so. If you'd rather go 8 weeks, fine, if you'd rather change after 5, go ahead, but give yourself enough time to get something out of a program before you mix it up. Don't abandon an exercise after just a week or two - you won't give yourself time to learn it well enough to get stronger from it.
Try a 6 week bodyweight only routine. Or kettlebell only. Do 6 weeks of heavy barbell training (squats, deadlifts). Do 6 weeks of low reps and lots of sets, then higher reps and fewer sets. Try some explosive movements. Switch from double leg moves to single leg moves.
There are good reasons to switch things around other than just avoiding stagnation. No single exercise selection or rep scheme or loading scheme addresses every aspect of fitness or strength. If you only do single leg exercises you're never loading your spine with much weight. If you only do double leg exercises you're not hitting the lateral hip stabilizers... ever. Every exercise will tax your muscles in a different way. Over the long haul, you want to be as well rounded as possible, just so you can prevent injuries. The same idea goes for the damage done by movements. If a particular movement wears on your joints in a particular way, if you do it every workout for year after year the cumulative trauma will cause an injury. Giving the joints a chance to recover by swapping out the exercise every so often will give your body a chance to heal.
Don't forget that there are also psychological benefits to changing your routine. New routines are fun - designing them, picking exercises, and so forth.
One caveat: Try to hit the major movements with every routine. Unless you're battling an injury, always include some kind of squat or squatting movement, some upper body push and upper body pull, and some core stability training. That still leaves you with lots of choices to make about how you'll hit all those aspects of training!