If you bought a retail Intel CPU, some paste is pre-applied to the HSF.
Some form of thermal interface material is always required because surfaces are often slightly curved and never perfectly smooth so without anything to fill gaps in-between, dry contact has very poor heat transfer properties.
In a non-conventional thermal interface roundup, the only common household product that is worse than nothing is chocolate. Margarine, mayonnaise, lipstick and toothpaste were all much better than nothing.
Of course, none of those are recommended for long-term use so if neither your CPU or HSF includes paste of any sort, go buy some.