Are we talking for a home cook?
If so I would rather see essential skills than just essential recipes, something like:
- Jointing a chicken, filleting fish, and some standard butchery skills
- Searing meat
- Tomato sauce as a base
- Understanding basic food hygiene
- Roasting and blanching vegetables
- Making a vinaigrette
- Basic chopping/knife handling skills
I think most of this stuff should be taught in schools to be honest, I remember cooking at school and it was around 95% cakes/cookies.
Is making a mayonnaise really necessary for a home cook? I agree with the rest though.
I personally don't think there are any essential recipes as such, and if there are they probably vary from culture to culture.
Are you trying to teach someone to cook?