I planted some berry bushes in my fenced-in garden a few years ago. I live in Northwest Montana. For the first two years nothing much happened. I would tie the new canes to the fence to control them and would get some berries, but never a lot. This year was a different story. Presumably as a result of a warm wet spring, combined with a cool wet summer, meant berries in abundance. I will, of course, remove the old canes.
Now that summer is over, the new canes have come in longer than I have every seen. These are the canes that are going to be bearing fruit next year. I have the choice of tieing the new canes to the fence as I normally do, but I would rather cut them back to 3 feet long and then tie them. Since some are almost 15 feet long that means cutting off a large amount of cane. Can I do that now and not impact next year’s production, or should I let them grow out to their maximum length and just deal with the overgrowth? These berry bushes are taking over my garden!
What kind of berry bushes? Management advice depends on species and variety - even if we assume you mean raspberries, the advice is different for summer vs autumn fruiting varieties.
… and if we assume blackberries then the advice will be to rip them out and beat the roots with a stick.
And don’t even ask about Snozzberries.
No love for Razzleberries? 
I’d shudder to compromise ANY berry production, but you have to be ruthless some times. Decide on a strategy NOW for making the canes behave themselves, then your pruning can be kept to the minimum. Install netting, 1x2’s, fencing, wires, trellises, whatever, and do a good job, you’ll thank yourself in coming years.
You can put out the word at picking time, I’ll bring my own bucket.
Assuming they are summer-fruiting raspberries - next year’s fruit is borne on this year’s growth, but specifically, most of it will be on the top one-third of this year’s growth.
If you prune back this year’s growth now, you’re likely to lose most of next year’s crop.
If the canes are too long, they can be run horizontally, then gently bent in a wide U-turn and trained back above or below the same horizontal run (above is probably more convenient in terms of picking the fruit and keeping it away from soil splash)
If you’re going to do that, sooner is better than later, as the canes will become less pliable as they age.
They are summer varieties of blackberries, raspberries and loganberries. Since they are taking over I need to drastically cut them back. If that means no berries next year so be it.
Yeah, it did seem a good idea at the time you planted them, didn’t it … alas, maybe it wasn’t.
Nuke 'em from orbit. Even then you won’t be sure.
(Grew up in a big yard that had been landscaped with blackberries and bamboo about twenty years earlier. Dear god, the battles.)
Every locality has its noxious weeds. Blackberries are native here, but not out of control.
My small woodland garden is plagued with an infestation of triquetrous garlic It spreads by seed and by bulb offsets - weeding it out by hand sets it back a bit, but if just one wheat-grain-sized bulbil is missed, it will rapidly recover ground.
My experience with blackberries is that you can severely prune them back and still have a bumper crop the next year. Nuisance weed on steroids, really. The others may require more delicate handling. My vote - decimate the blackberries, and tie back the canes for the raspberries. If you really want to be scientific, you could try doing some of each to all varieties and take note of the results.
FTR, I hate my blackberries - the bushes. The fruit is fine. We eat it all summer. The bushes are clearly demonic. If the zombie apocalypse ever comes, we will not have to worry about defending that side of the property. Nothing is getting through.