What computer games do people use for mental exercise ?

If you do the brain exercises, keep in mind that they are exercise, not intense effort. Brain challenges are often too intense. You do not want to get frustrated and sense failure. In fact, you want just the opposite. You want to do tasks where you will be successful most of the time.

Research shows that games the exercise quick processing are better than games that challenge with intensity. I play Minesweeper medium against the clock because it challenges me to be quick without high difficulty.

These are my favorites:

I did a lot of Windows Solitaire, Spider Solitaire (intermediate, two suits), FreeCell, Minesweeper, and such. They are included with most versions of Windows. There are downloadable versions also available. You can do them as fast as you like. They exercise multi-step processing.

I do a lot of computer based jig saw puzzles.

Jigsaw - Jigsaw - MSN Games - Free Online Games
I use the edges function then the arrange function so I don't have to sort the pieces. I shoot for 7 minutes but different puzzles can take up to 20 minutes. I do 3 every day.

and Free Jigsaw Puzzles - Jigsaw Puzzle Games at Free Jigsaw Puzzles - Jigsaw Puzzle Games at TheJigsawPuzzles.com - Play Free Online Jigsaw Puzzles I choose the 100 piece puzzles.

Also, Scrabble known as Just Words Play Just Words Online - AOL Games You can set the difficulty so the computer plays at your level.