I'm in the process of gathering up all my important documents to move abroad and I was wondering if it's legal, or even necessary, to print extra copies of things like my birth certificate, driver's license, social security card, etc. If so, do I need to get them notarized?
Also, I read I should take my tax records with me but the only papers I kept are my W2 forms. Is that all I need or should I seek out forms from the IRS to request my tax records? If so, how many years back should I request?
I've done this a few times, and I always pack notebook on my carryon with a copy of pretty much every important/useful doc that I can think of. Mostly it isn't needed, but it really sucks to be in a spot where you need something and don't have ready access to it. Even docs that you carry with you, like your DL and passport, you should have a paper copy (in a separate spot) just in case your real one gets stolen/lost.
Generally speaking, other than your passport, no one in other countries will care about/trust your US documents, notarized or not, unless they've specifically asked for something. (A federally notarized fbi background check, or diploma copies notarized at an embassy of the country you're moving to, as examples.) And your tax info,if needed, is probably needed to verify income/employment (If you do need that, in addition to the W2's, I would have access to a few months of pay-slips since that's probably easier to understand and verify than a W2.), but if you're moving, then you would normally not have that source of income any longer. So I wouldn't worry about ordering past W2's unless something has specifically asked for it. If you need to provide proof of finances, then you would probably want bank statements.
There are a few different considerations too. First is the immediate stuff that you'll need for the country, and that will vary hugely depending on where you're going and for what reason. You should know this before going though, obviously (and should be meticulous about having exactly what their immigration say you need), but there are a few things that you might not think of. First, the immigration people have never really followed what was on their site, so don't freak out when they expect you to have stuff they didn't mention and don't care about half the stuff they did. It's just how government works everywhere I guess :/
But aside from whatever you need to get your resident status, you'll probably also need other things like a bank, driver's license, apartment, etc. These things may need stuff like prior leases and landlord contact info, proof of income and past employment, etc. etc. Note that some of these things are WAY harder in other countries, and as a bonus, no one will trust you because you're a dirty foreigner

But try to think of everything that you'd need to start a new life in the US, and be sure to have that stuff handy. Just to be safe, I would try to carry a physical copy as well as having everything scanned and available in dropbox or somewhere online, just in case I need it.
The other side to that, is that you'll still need to manage stuff in the US once you're gone. You'll still need to file taxes, probably pay some bills, etc. So you'll need to have everything on hand to be able to do that. Not sure if you've traveled much internationally, but I would also recommend getting a US-based vps/vps before you go (and don't forget to notify your banks). When you try to do things from abroad, stuff can be oddly difficult sometimes. Pretty much everything you do with the American sites that you're used to using will now flag your account for fraud because you're trying to do it from a different country. Being able to log in with a US ip can be a lifesaver sometimes.
Feel free to ask if you have any other questions.