How can I identify games that would work better on the computer?
Computerized board and card games can have an advantage when it enables automation of what would otherwise be mundane or tedious tasks:


Shuffling cards in Dominion is a good example; eliminating shuffling applies to lots of classic card games that have wide on-line audiences like hearts, spades, etc. 
Computer versions also work well if they can abstract away math that is part of the game, but not really a part of the strategy. Think about a game where anyone at the table would be comfortable helping someone get the calculation right; a benign example would be calculating the 10% income tax in monopoly or figuring out the price to unmortgage a property.
Some players don't like the uncertainty involved in games with lots of dice rolling or probability calculations because they're not comfortable enough doing them in their heads to enjoy playing in person. Obvious examples include gambling games like poker or war simulations like Axis and Allies, both of which have active and thriving on-line communities. 


Attributes that make a game ill-suited to being played on a computer:


A high degree of player interaction, especially if characterized by collaboration. Examples would be Arkham Horror (highly collaborative) or Pictionary (lots of in person interaction)
Games where access to the internet completely ruins them: Trivial Pursuit and Scattegories come to mind, as does Balderdash.
Games where a significant fraction of the enjoyment comes from the atmosphere created by playing, like Arkham Horror or Betrayal at the House on the Hill.
Games where players need to take in a lot of information at once. As Edward Tufte likes to point out, the resolution of the physical world is still much greater than the resolution of a screen and most board games take up much more real estate when played than a typical monitor size. I've never played, but looking at all the pieces in the box, Twilight Imperium seems like a potential example, and even playing Axis and Allies on the computer can suffer from a hindered ability to "see the whole board".