"I.e." and "e.g." don't mean the same thing.
E.g. means “for example,” so you use it to introduce an example: I like card games, e.g., bridge and crazy eights. Because I used e.g., you know that I have given you a list of examples of card games that I like. It's not a finite list of all card games I like; it's just a few examples.
On the other hand, i.e. means “in other words,” so you use it to introduce a further clarification: I like to play cards, i.e., bridge and crazy eights. Because I used i.e., which introduces a clarification, you know that these are the only card games that I enjoy.
Here are two more examples:
Squiggly loves watching old cartoons (e.g., DuckTales and Tugboat Mickey). The words following e.g. are examples, so you know that these are just some of the old cartoons that Squiggly likes.
Squiggly loves watching Donald Duck's nephews (i.e., Huey, Dewey, and Louie). The words following i.e. provide clarification: they tell you the names of Donald Duck's three nephews.
An important point is that if I've failed, and you're still confused about when to use each abbreviation, you can always just write out the words "for example" or "in other words." There's no rule that says you have to use the abbreviations.
Dos and Don'ts
Don't italicize i.e. and e.g.; even though they are abbreviations for Latin words, they've been used for so long that they're considered a standard part of the English language. Also, remember that they are abbreviations, so there is always a period after each letter.
Also, I always put a comma after i.e. and e.g. I've noticed that my spell checker always freaks out and wants me to remove the comma, but five out of six style guides recommend the comma. Seriously. I got so engrossed in the question of whether a comma is required after i.e. and e.g. that I made a table for the website summarizing the opinions of six different style guides.