Let's cut out the introduction and get right to it.  Be advised that most of these picks are based on images I've transferred back to disks when possible.

• Bubble Ghost - a game I once played on GameBoy, this game involves guiding a bubble through single screen mazes filled with obstacles that can burst your bubble.  Pop the bubble and it's game over.  Very colorful and enjoyable.
   
• Buggy Boy - The ST is the only system I've come across that has this simple little driving game.  Collect flags, gain more time while avoiding rocks, walls, and water.  Lacks the computer controlled vehicles found in the arcade but the real of it is here.
   
• Spellbound - This side-scrolling adventure game has you solving levels to advance. You can carry only one item at a time and falling from high places can hurt you as well as the enemies in the levels.  And you only have one life. Plan your strategy carefully.
   
• Atax - A vertical shoot 'em up with a few elements from the likes of Gradius.  Colorful and sounds good.  Everything in the game is a hazard including the environment objects.  
   
• GODS - This side scrolling adventure is one I owned for a 386 PC.  The ST version looks and sounds really great and takes advantage of the hardware in a good way.  Each level is huge and includes enemies, bonus items, and hidden areas and objects.
   
• Nitro - A neat top-down racing game that I am not very good at...but I keep coming back to this one.
   
• Populous - A one on one strategy game where you have to modify the landscape for your people to populate and prosper.  As you people grow the more problems you can create for your enemy from floods to creating a volcano.  Gets a bit sluggish on the ST when too much is going on but still fun.
   
• Vroom - An impressive F1 racing game with a view from the driver's seat.  Easy to pick up and play. Can be challenging.  Amazing speed!
   
• F1 World Championship (Domark) - Believe it or not, Vroom has a brother.  This one doesn't track lap times.  Game mechanics and goals are the same.

More to come as I discover them.  I have a LOT more to try out.  What's your favorite Atari ST games so far?