Are there any exercises that engage all or almost all(about 50%) of your muscles? If there are any exercise like this what are they called?
Assuming that you're talking about weight based exercises only, my answer would be no: there is not a single exercise that works every muscle.
My reasoning for this is that your body is made up of agonist/antagonist muscle pairs. Think bicep and tricep. They work together but oppositely. If you flex your bicep and tricep at the same time, you stay static. For this reason, I believe it isn't possible to work out every muscle. At a minimum, I believe you'd need two ridiculous movements to cover every base.
In practical gym workouts, I think the closest you'd get would be with compound exercises. These are multi-joint multi-muscle-group workouts. Things like deadlift, snatch, clean and press, bench press, etc.
Yes*, they're called complexes.
Before I get into complexes, and the caveat, an argument could be made that pretty much any of the power lifts or olympic lifts engage almost all of your muscles (assuming you're training close to your max and using full body tension during the lift).
Think, leg drive in the bench press, driving the elbows up in the front squat, grimacing while pulling a heavy deadlift (engaging the facial muscles). Want big arms? Work up to a 600lbs deadlift or squat.
A complex is a series of movements chained together to form a single rep. An example with a barbell would be:
deadlift > bent over row > clean > front squat > overhead press > good morning > behind neck press
A kettlebell complex (double kettlebells) could be:
bent over row > clean > front rack walk > front squat > overhead press > waiter walk > collapse
Bodyweight? Slightly tougher but with a bit of imagination:
laying face down under a chin up bar > press up > burpee (grab the bar) > leg raise > muscle up
*it depends on your definition of an exercise. If you want a single, recognisable movement, then I'd say the Olympic lifts are your best bet. Mind you, you could argue that the bear is a single, recognisable movement.
Some complexes have you perform multiple reps of a movement before moving onto the next in the chain, being pedantic, I wouldn't say they count, but a single movement flowing into the next does. After all, what is a clean and jerk other than an explosive deadlift, front squat and overhead press into split squat :)