Not quite. If you aren't competing in powerlifting, there's no rule that says you have to squat, bench, and deadlift. For people who just want to get generally stronger or in better shape, the traditional big 3 may not be the best option. Whether it be due to previous injuries, disadvantageous leverages, or a simple dislike for one of the big 3, people can have legitimate reasons for choosing other lifts to replace the big 3. In particular, the like or dislike for the lift is a huge factor. If you truly hate a lift, you're simply not going to give it your best.
I will say that nearly everyone can do the big 3, if they become technically proficient with a form that's safe and makes the best use of the person's leverages. But that doesn't mean the big 3 are the best option for every person for the sake of getting jacked or in shape. For example, a tall, lanky guy might have trouble with the barbell back squat as his main leg movement. So might someone with a pre-existing herniated disk. For these people, a belt squat or even a leg press may be a better option for the quads.
Additionally, I think it's better to use 4-5 main movements to gauge progress rather than just 3. A "Big 3" keeps things simple, but a Big 4 or Big 5 makes sure all bases are covered, still without overcomplicating things.
I'm by no means the first to come up with this idea.
Ben Bruno introduced the idea of finding your own "Big 3 lifts" in a very well-thought out article here. He said that your "Big 3" could be changed up every several weeks to prevent overuse injuries. This is a good idea, but I'd suggest choosing some lifts that you can stick with for a long period of time in order to consistently be able to gauge your progress as the years go on.
Jim Wendler, one of my favorite writers about lifting and being in shape, introduced the idea of a "Big 4" with his classic 5/3/1 program. He included the standing barbell press as his 4th lift after the squat, bench, and deadlift. The standing press is an awesome exercise, and is good for training the shoulders in a different plane than the bench press in order to keep them healthy and strong. It's really a full-body exercise, and if you can do the Big 3, it's a solid option for your Big #4. Some might say that having 2 pressing movements is redundant, but I believe that pressing should be trained with a decent amount of variety since it can be done in so many different planes of motion.
Don't fuck with this man.
As some may know, I was a personal trainer at a gym this summer and I'm still doing some limited private training. I would generally try to find 4 or 5 movements that my clients could safely do, and with these movements cover the major planes of motion as effectively as possible. The performance of these lifts would be my primary means to measure strength progress. It was important to find movements that were somewhat easily learned, especially with the limited time I had with each client. Some people will just take forever to learn how to back squat with a barbell, and the cost to benefit ratio of teaching the lift just doesn't pay off.
When selecting your big lifts, each movement should fulfill some particular criteria:
1) Compound movement: Each of your big lifts should be a big, multi-joint movement that involves a large number of muscles. Additionally, there should be significant potential to progressively overload the movement (e.g. any barbell exercise). No concentration curls as a main movement.
2) Free weights (preferred): Each big lift should be with a barbell (best) or dumbbells (still good) where possible. If, for some reason, you're so messed up that you can't do any free weight exercise in a certain plane of movement, certain machines might be permissible.
3) Bilateral... except for some: Your Big 4/5 should be mostly bilateral movements, since they allow for the most weight to be used. With many unilateral moves, you'll be too focused on keeping your balance to use any significant amount of weight. However, certain unilateral movements are "big" enough to be primary lifts. These include lunges and split squats as "squats", one-arm rows (dumbbell or Meadows variations), one-arm standing presses, and one-arm cleans and snatches. Of course, if a unilateral movement is chosen, reps and weights should be kept equal on both sides.
4) Safe and pain-free: This is simple. If a movement causes you pain during or after a workout, don't do it.
5) Enjoyment factor: You should like doing this lift. If you don't enjoy it, it's going to be a drag forcing yourself to do it every week.
6) Dissimilar enough to your other movements to justify its inclusion: This movement should work an area that the other exercises fail to stimulate sufficiently.
As mentioned before, your entire body should be covered by your main lifts. There are a few ways you might go about selecting what types of movements your big lifts should be. Using any of these templates, your entire body will be effectively covered.
One way is to do it like Wendler, using a Big 4 and 2 presses:
Squat
Press 1
Press 2 (in a different plane than Press 1. So if Press 1 is an incline press, a good option for Press 2 might be a dip)
Hip hinge/deadlift
Here, upper body pulling would have to be done as assistance work rather than programmed as a main movement.
Another way is to replace the second press with an upper body pull as a main movement, a la Carter:
Squat
Press
Hip hinge/deadlift
Upper body pull
Another option is to combine these two, using a Big 5 (my favorite option)
Squat
Press 1
Press 2
Hip hinge/deadlift
Upper body pull
Or if you really want to work on your back and pulling strength...
Squat
Press
Hip hinge/deadlift
Upper body pull 1
Upper body pull 2
If your first upper body pull is a chin-up or pull-up, your second pull should be a row, clean, or other more upper-back/trap focused movement.
Some options for each main movement listed include, but are not limited to...
Squat (Movers: quads, adductors, glutes)
Barbell back squat (high bar or low bar)
Barbell front squat (any grip variation)
Goblet Squat
Belt Squat
Lunge (walking, reverse, or forward)
Split Squat
If you have to do a machine...
Leg Press
V-squat machine
Hack squat machine
Press (Movers: pecs, delts, triceps)
Standing or seated military press (barbell or dumbbell)
Bench press (flat, decline, incline) (barbell or dumbbell)
Behind-the-neck press
Push press
Push-up
Dip
Handstand push-up
Machine options are pretty diverse. Hammer strength is probably your best bet.
Hip Hinge (Movers: glutes, hamstrings, some quads for non-stiff-leg DLs; entire back hit as stabilizers)
Deadlift
Snatch-grip deadlift
Deficit or elevated deadlift
Trap bar deadlift
Stiff-leg or Romanian deadlift
Good mornings, all variations
High pulls
The "machine" options here aren't really machines, but rather specialized benches used for bodyweight movements:
Reverse hypers
45 degree back extension
GHRs
Upper Body Pull (Movers: lats, traps, small upper back muscles, delts, biceps)
Barbell row
Dumbbell row
Meadows row
T-bar row
Inverted row
Dumbbell or barbell hang power clean
Dumbbell or barbell hang power snatch
Chin-up and pull-up of all grips
Upright row (dumbbell or barbell)
Machine options:
Lat pulldowns
Chest-supported row variants
If you use any of these templates with these exercises, all of your major muscle groups will be hit. Where one exercise may fail to hit a muscle effectively, the other exercise should make up for this. For example, if you decide to use upright rows as an upper body pull, your lats will be neglected unless you choose to include a second upper body pull, or choose a deadlift as your hip hinge (provided you effectively use your lats when you deadlift).
Small muscle groups like rear delts, medial delts, abs, calves, forearms, and biceps might not get hit quite as hard as you'd like with just your Big 4/5. That's ok - that's what assistance work is for. These can be hit lighter for higher reps after your heavy work with the main movement, or as a warmup beforehand.
As far as setting up an actual program with your Big 4/5, it doesn't matter if you wanted to devote an entire day to each lift (followed by assistance), do the lifts together multiple times per week, or something in-between. Pick your big 4/5, get really damn good at them, and do some lighter, high-rep stuff for filling in small muscles.
Now go lift.
