Originally a Half-Life Mod: They require the Half-Life engine (GoldSrc/Source) to run.
Standalone Releases Exist: Valve later sold them as standalone products on Steam. You do not need to own Half-Life separately to play these Steam versions today.
Non-Steam/Pirated Versions: Often require a cracked Half-Life install (illegal).
Modern Counter-Strike (Global Offensive / CS2)
Fully Standalone: Built on Source 2 engine; no Half-Life ownership required.
Free-to-Play: CS2 is free on Steam.
Summary: For current official versions (CS2, CS:GO), Half-Life is not required. Only very old, non-Steam versions of the original mod might demand it.