I know 4e's skills, and they infrastructure within which they are used, don't map extremely well to 5e but I figured I'd include some data from my PBP on here. Interesting to look at if nothing else.
There are some things of note that will skew the results considerably in favor of some skills over others. Those are:
1) This is a single player game (but with a companion bear for some of it and now a companion assault team - swarm). All of the below checks are solely for player controlled characters. If this included NPCs, Athletics and Acrobatics would jump up a bit due to their combat use (my combats, and 4e combats generally, involve a decent bit of physical checks).
2) The single character is a Fighter with Nature Rituals, a History reroll utility, an Athletics utility (combat and noncombat application), and a broad swath of competency across all skills but the Charisma skills.
3) Play is heavily on exploration challenges/adversity and has only included 1 full parlay SC and 1 interrogation that was part of a greater challenge.
I should note, this data is not representative of my home games. In my home games, I would soundly rank Arcana, Athletics, Insight, Nature, and Perception as, by a far margin, the most potent and most broadly used/applicable skills - so I guess A. Acrobatics (stunting, grapple checks, and all of its typical stuff), Dip/Intim are about split, Endurance (due to required exposure checks/hazard contermeasures, Disease Track checks, and Group Checks), Stealth, Streetwise, and Thievery are a tier below those - so I guess B. Everything else is probably C or situationally B. The only skill that doesn't get a ton of play in my home game is Heal. It is basically used for forensic investigation, kissing NPC boo-boos (figuratively), and subbing in for Endurance checks on the Disease Track (when the caretakers Heal is better).
Without further ado, the aforementioned PBP data:
SKILL | PASSIVE | TASK/RITUAL/COMBAT | GROUP | SC |
Acrobatics |
| 2 |
| 3 |
Arcana |
|
|
| 2 |
Athletics |
| 7 |
| 6 |
Bluff |
|
|
| 1 |
Diplomacy |
|
|
| 1 |
Dungeoneering |
|
|
| 2 |
Endurance |
| 3 | 1 | 1 |
Heal |
|
|
| 3 |
History |
|
|
| 2 |
Insight | 1 |
|
| 2 |
Intimidate |
|
|
| 4 |
Nature |
| 5 |
| 4 |
Perception | 5 | 2 |
| 2 |
Religion |
|
|
| 1 |
Stealth |
| 1 |
| 3 |
Streetwise |
|
|
| 1 |
Thievery |
| 1 |
| 1 |
EDIT - Didn't include Nature as top tier in my home game.