AMX Mod X uses rolling releases, and updates are continuous. Updates to stable versions of AMXX are small and non-disruptive. It is generally recommended to run the latest stable build, however, it is not necessarily urgent to upgrade when a newer build appears.
 
For general upgrades, you should make sure you:
Read the changelog!
Replace all binaries.

• dlls, modules / *.dll/*.so - This includes amxmodx_mm and all modules.
  
• plugins/*.amxx - Any default plugins AMX Mod X comes with.
  
• data/GeoIP.dat - If you use GeoIP, make sure you update the database.
  

Replace language files.

• data/lang/*.txt - Important to make sure plugins are using the right language phrases.
  

Read the upgrade notes to see any other custom changes needed.
If you do scripting locally...

• Replace all base include and source files (.inc, .sma).
  
• Replace the compiler and its binaries (amxxpc, amxxpc32, amxxpc64).