I just started "Even More Incredible Machine" last night, and I probably completed 30 or so puzzles. Now I'm having trouble remembering where I left off. When I go to "select puzzle," numbers 1-88 are green (available) and 89-160 are red (locked). But I know for certain that I didn't finish 88 puzzles.
So my question is: does EMIC track what puzzle I was on or do I just have to remember? Also, do the other games in this pack track which puzzles you have and have not completed?

To pick up right where you left off you need to enter the code given after you complete a puzzle. These codes store both the puzzle you're on as well as your current score (first word is for the puzzle, the gibberish is for the score).

If you have been completing them in order it will have the number of puzzles completed in the bottom left of the control panel. To keep track in the other games your best bet may be to note down on a bit of paper what puzzle you are on or make a notepad entry for your desktop.

The first 87 puzzles are the old TIM1 puzzles. In TEMIM, they are marked as completed so that you can jump right into the new puzzles without having to complete the old TIM1 puzzles.
So if you started with the old TIM1 puzzles, you're going to have to keep track of which ones you finished yourself. But once you start on the new TEMIM puzzles, it will keep track of your progress through those properly.
The rest of the games in the series should keep track of your progress just fine.