So you want low resource demanding games?
First of all you could use this
site for searching some newer games. It will tell you your specs too.
I only have old computers lying around some old/low graphics games are somewhat of a hobby...
Here's some games you can take a look at:
- Battlefield 1942 - FPS game that started the Battlefield series off to a nice start. It has bots so no worries if you have bad internet.
- Civilization 2 - Stratagy/Turn-based game that's pretty old but it is pretty fun.
- Half-life - FPS with a load of mods if you get through the awesome storyline.
- Cave Story(Doukutsu) - Originally Japanese I think but there is an English translation available. It's pretty awesome because it's got a great story and a Metroid-esque gameplay.
- Dwarf Fortress - Text-based gaming to the max. This game has loads of stuff to learn and loads of replay value. The learning curve is steep though. Don't expect to become a master in one day. Also use Dwarf Therapist.
- Ace of Spades - FPS that's got guns and blocks (Minecraft style but the blocks can fall if there is nothing holding them up!). Jagex has taken over development but expect to see the classic AoS return someday...
- Sim City 2000 - A classic city building simulator. Gotta love it.
- Roller Coaster Tycoon - A theme park simulator. Gotta love this too.
- Thief: The Dark Project - Stealth game set in a medieval/steampunk realm. When I saw that Dishonored game I remembered this priceless gem.
- SpaceChem - a Zachtronics game (Zach made Infiniminer that inspired Notch to do Minecraft!). 2 parts Chemistry + 3 parts puzzles --> 1 part awesome
- Lone Survivor - A pixely game that follows a character in a zombie apocalypse. Haven't beaten this one or played it much.
Those are just some old games or low resource intense games that you might be able to run.