Upvote:7
Assuming "air services" means scheduled flights and not just chartered helicopters etc, off the top of my head we have:
I believe that may actually be it, since (AFAIK) all Pacific, Caribbean and African microstates do have airports. There are some territories like Pitcairn and St. Helena that don't, but none are independent.
Palestine may also qualify if you consider it a country, since all airports in Gaza and the West Bank have long been non-operational.
Edit: And of course it's already on Wikipedia! https://en.wikipedia.org/wiki/List_of_countries_without_an_airport