In my case at work the stuff I create is used internally, so I can rely on the average business workstations which are deployed throughout the various locations.
For my personal projects I test on an 8 year old i5 with intel junk graphics and 4GB, my wife's cheapo $300 laptop with intel sucky graphics, and on my own workstation with a nice 1080GTX. Mobile I ask friends and in particular nephews and nieces to playtest on their iPads.
I check memory and CPU performance with Process Explorer, and in the game engine debugger (if it has one). If the game works okay'ish on the 8 year old junk intel i5, I know I am good ;-)
But really, there nothing like having other people with various hardware setups play test your projects.
On a side note: quoted system requirements for any given game rely very much on the perception of the developers if they feel it is acceptably playable. I recall the minimum requirements for a game like FarCry not exactly giving a player a good experience - some would say minimum requirements are all over the place for games in terms of a "playable" experience.
And obviously it very much depends on the type of game: I don't mind playing Dungeons of Dredmor on that old i5 of mine, and while it can slow down at times, it doesn't really impact the player experience as much as trying to play a fast arcade game that should be running at 60fps.