Ability checks, those things that power the skill system of 5e. In this article I would like to explain why I think they are basically worthless, and that within old school roleplay, particularly within the rule system of Old-School Essentials, there is almost always a better choice.
The referee may use a character’s ability scores to determine the character’s chance of succeeding at various challenging tasks.
Rolling an ability check: The player rolls 1d20 and, if the result is less than or equal to the ability, the check succeeds. If the roll is greater than the ability, the check fails.
Modifiers: Bonuses or penalties to the roll may be applied, depending on the difficulty of the task. A modifier of –4 would be a relatively easy ability check, and a +4 would be very difficult.
— Old-School Essentials
Now the rules out of the way, lets talk about peoples insticts. Players coming from more modern editions of D&D will often see this, then port over their instinct to call for 5e style ability based skill checks as an ability check. I'm now going to propose alternatives that I would assert fit better within the game.
In OSE, I would suggest you to consider the peril in place. If the peril is instant death (drowning, falling to your death), consider using a save versus death. If the penalty is delay, perhaps consider a save versus paralysis or be delayed. If the penalty is non existent, let it happen. For lifting a heavy object, I would recommend you set a strength rating required to lift it, either the person has it, or they need to work as a group to have it.
Acrobatics in 5e is used to be nimble, running across ice, balancing on tightropes, and keeping in general just keeping your footing. For most circumstances you'd lean on acrobatics I'd recommend simply allowing the person to succeed, or applying a penalty in exchange for them succeeding. Perhaps a -2 to attack rolls if fighting on an unstable circumstance. Simply change the environment and how they interact with it, rather than giving them a save. Otherwise, if the acrobatics is to grab a bar and not fall to their death, death save, maybe paralysis save, same as in Athletics.
Slight of Hand
Thieves pass at this automatically. Nobody else should be trying it. If it's being used to pick pockets, thieves have a pick pocket skill they can use.
Stealth is baked into the game already, it's called surprise, it's a badly worded stealth mechanic. See my article on the thief.
Arcana, History, Nature, Religion
These are all knowledge skills. I would recommend simply giving knowledge freely depending on the class enquiring and their level. Remember that not knowing something is in general less fun than knowing it. The Magic-User will know an arcana fact, or perhaps might need to be a higher level before they would know it. A thief a history fact. A halfling or elf a nature fact. A cleric a religion fact.
This is covered by the games searching mechanics, giving you a 1-in-6 (improved for some demihumans) to find hidden things in a 10' by 10' region over 10 minutes of searching. However, if the player describes themselves looking in a place the thing is in, just reveal it. The search mechanic is more of a crutch for when they don't have any ideas. If they say they push all the tiles on the wall, and that is how the hidden door is operated, have them succeed automatically and find the hidden door.
Make a reaction roll for the animal. Maybe give a +1 bonus if the character is an appropriate class.
This one is a little strange to be honest. I think most of the time you're going to already know the disposition of a person based on their reaction to you. If the party is suspicious of someone, perhaps have them ask about body language. Describe them being a bit sweaty or constantly glancing about, rather than putting that information behind an insight check. Same logic as the knowledge checks, noticing is almost always going to be more fun and interesting than not noticing.
This is a knowledge skill, same as the rest of the knowledge skills.
Again, we can use a similar approach we used to investigation, in addition to that, surprise forms the basis for perception and stealth, and so these both complement each other in using surprise instead of either of them.
Adventurers should general be competant and have the basic wilderness skills they will need to survive. For more advanced skills (predicting the weather, tapping a tree), I recommend simply considering the class of the character and whether or not it seems appropriate based on what has already been established about them. A woodsman should have a pretty good beat on the weather, a man from the far north should know how to spot a crevasse.
Deception, Intimidation, Persuasion, Performance
Charisma checks can pretty much universally be replaced by reaction rolls for the person being influenced. Maybe a morale check if the party is doing something really scary for intimidation.