A point of uncertainty for many: when you have something listing examples, do you use etc. with e.g.? For example,
requirements for baking a cake (e.g., eggs, flour, sugar, etc.)
The answer: use one or the other (or neither – see below), but not both. Each of them indicates you’re seeing a subset: e.g. translates (roughly) to “for example”, and etc. translates to “and more” or “and others”.
Faced with a sentence that uses both, I generally drop the etc., although in some contexts I’ll drop the e.g. And in some contexts I’ll use for example or for instance in place of e.g., or and more or and so on in place of etc. (I will not, of course, have for instance, flour, eggs, sugar, and so on, for the same reason as given above: you only need one – otherwise you’re saying and so on is an instance or example.)
When deciding which to drop, note that etc. may seem more hand-waving dismissive (as may and so on) and e.g. more high-toned or business-y; also, e.g. declares from the outset that the list is not exhaustive, whereas etc. waits until the end to show that there’s more, so there’s a difference in the flow of the argument.
Another thing to pay attention to is whether the list is definite or possible members of a set. Generally, you will find that etc. tends more to imply that the things listed are all definite members of a fixed set, whereas e.g. is more able to allow possible members of a set. Compare:
Choose some music you like (e.g., Pet Shop Boys, Metallica, Beethoven).
Choose some music you like (Pet Shop Boys, Metallica, Beethoven, etc.).
The second is more likely to imply that you like all three of the artists listed, whereas the first tends more to allow that they’re just examples of music you might like.
And if we look back at the cakes, we can try both:
requirements for baking a cake (e.g., eggs, flour, sugar)
requirements for baking a cake (eggs, flour, sugar, etc.)
The first allows that you might bake a cake without one or more of the items listed, whereas the second tends to imply that they’re all requisites.
Oh, and what about i.e.? That’s from Latin for “that is”, and it means you’re presenting not an example – not a subset – but an amplification or restatement. Let’s look at our examples:
Choose some music you like (i.e., Pet Shop Boys, Metallica, Beethoven).
requirements for baking a cake (i.e., eggs, flour, sugar)
In the first case, it’s saying that those three are the music you like and the music you’re going to choose, and none other in addition. This is possible but unlikely. In the second case, it’s saying that you need nothing other than eggs, flour, and sugar to bake a cake. Heh… you try that and tell me how it comes out.
If you want to be less prissy, i.e. can be replaced by in other words. Also, there’s nothing in the logic of a sentence to keep you from using i.e. with etc., but it’s sloppy writing – better just to use e.g. and no etc. Oh, and often you can drop it altogether:
He named the three hottest women in film in his opinion (Cate Blanchett, Rosamund Pike, and Lucy Liu).