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?
Is making a mayonnaise really necessary for a home cook? I agree with the rest though.
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.