Guides/GoldSrc
This guide will explain how to take HUD-less screenshots on GoldSrc-based games/mods.
For all common games, you can just type map [mapname] in the console (as long as you have never previously opened another map). You will appear as if you were in Half-Life, without weapons and without HUD. Then you can just use sv_cheats 1 along with noclip (this sometimes requires you to restart the map) to freely navigate the map.
HL Rally
Unfortunately this mod doesn't have a free-look spectator mode and doing noclip with sv_cheats feels broken as this mod doesn't have vertical movement.
The only way to take HUD-less screenshots on this mod is copying all the maps files to Half-Life and launching them from there with the common commands listed at the beginning of this article.