As long as you don't use the other accounts to circumvent any limits or do anything you can't do with a single account, or use the accounts to create a misleading impression (e.g. by commenting on or answering your own posts), multiple accounts are tolerated. But they should never interact in any way.
In practice, it is very easy to accidentally misuse multiple accounts, if you are actively using them. You have to pay attention to never vote on the same post or interact in any other way. Using another account to post a question anonymously is usually unproblematic, but that account should not vote or do anything else to avoid breaking the rules.
If you accidentally created those accounts, you can merge them.
A post on this topic from Robert Cartaino, an SE employee:
Multiple accounts are generally not allowed, but we (Stack Exchange)
have yet to take an absolute, hard-line statement against having
multiple accounts. Some feel they have a need to separate (for
example) their public from their personal lives. I can't think of
another valid use case, but know that neither our system nor our
Terms of Service support having multiple accounts and they are
subject to removal or merging at any time.
So if you want to live on that bleeding-edge case, there are some
absolute, immutable rules you have to be vigilant about if you
want to continue using the system.
The Golden Rule The #1 absolute rule is that those accounts should *NEVER* in no way interact with each other in any way.
Period; exclamation point. Trying to do anything with a second
account that you could not do with one account is a good way to get
your account suspended and deleted unceremoniously. That includes
voting multiple times for a post, casting multiple close votes or
flags, exceeding your personal allotment of activities (daily voting
limits, questions, close votes, etc)… and this prohibition
goes triple-y so for sock puppet voting (i.e. voting for your own
posts). That is a big, huuuge no-no.
#2, Don't fake it Our Terms of Service prohibits impersonating another person. If someone were to suspect your intentions, don't
exasperate it by "faking" a bunch of phony profile information. The
response may be stronger than warranted by your actual intentions.
"Faking it" also includes pretending to be two people where the
content is concerned. Don't support yourself in comments, don't answer
your own questions, don't stir up staged controversy (or quell it by
playing a supportive peer) and — I say this again because it is
so important — do not up-vote your own comments (or posts!).
The more I write this up, the more I realize just how problematic it is. I would really prefer just to say "don't do it"… at
least until we implement a way to gain the benefits without all the
potential for abuse.