E.g. stands for exempli gratia, Latin for for example. It is used to introduce examples.
I.e. stands for id est, Latin for that is. It is used to introduce a definition or clarification.
Sometimes i.e. is used to introduce examples, but this usage is incorrect. The confusion probably arises from i.e. and e.g. having slightly similar functions.
Although the abbreviations serve their respective purposes adequately, the full English translations that is and for example are also fine in most writing contexts. Indeed, using the full forms helps avoid overuse and confusion.
Neither i.e. nor e.g. is well suited to speech, but both are recommended for parenthetical text (i.e. it is better not to use that is or for example to introduce something in parentheses). Both terms, whether abbreviated or not, are usually preceded by a comma. In American English they are often followed by a comma, and sometimes by a colon.
Something else to watch out for: since e.g. introduces a list that is representative only, it is redundant to conclude the list with etc.