What are the Doctor's "Rules"?

Question

Rule #1: The Doctor lies.

What are his other rules? Is there a definitive list anywhere?

Answer 1

Working from the link given in @Richard's comment, I've compiled the following list. Note that not all the 'rules' listed in the Wikia page actually deserve to make the cut: some of them aren't actually cited as Rules, just as "wise-sounding things the Doctor says", which could cover almost anything; some of them don't actually appear in the episodes as cited by Wikia; and I also ignored the one rule which was cited to a prose story rather than the main canon of the TV series.

Fourth Doctor

Rule #1: do exactly as I say.
Rule #2: stick close to me.
Rule #3: let me do all the talking.

DOCTOR 4: Good. Now, pay attention. I'm not anticipating any trouble, but it's as well to be prepared for these things. Ground rules. Rule one, do exactly as I say. Rule two, stick close to me, and Rule three, let me do all the talking. Is that perfectly clear?

_{-- The Ribos Operation (Old Who, Season 16)}

Seventh Doctor

Rule #1: I'm in charge.
Rule #2: I'm not the Professor, I'm the Doctor.
Rule #3: [unidentified]

DOCTOR 7: But there are three rules. One, I'm in charge.
ACE: Whatever you say, Professor.
DOCTOR 7: Two, I'm not the Professor, I'm the Doctor.
ACE: Whatever you want.
DOCTOR 7: And the third. Well, I'll think up the third by the time we get back to Perivale.

_{-- Dragonfire (Old Who, Season 24)}

Tenth Doctor

Rule #1: don't wander off.

DOCTOR 10: Rose! Mickey? Every time, every time, it's rule one, don't wander off! I tell them, I do, rule one! There could be anything on this ship!

_{-- The Girl in the Fireplace (New Who, Series 2)}

Eleventh Doctor

Rule #1: don't wander off OR the Doctor lies.
Rule #7: never run when you're scared.
Rule #27: never knowingly be serious.
RUle #408: time is not the boss of you.

RORY: The Doctor's always saying "don't wander off." First rule with him, actually, "don't wander off".

_{-- The Rebel Flesh (New Who, Series 6)}

DOCTOR 11: Oh, you should always waste time when you don't have any. Time is not the boss of you - Rule 408.
[...]
DOCTOR 11: Never knowingly. Never knowingly be serious. Rule 27. You might want to write these down.
[...]
DOCTOR 11: Please, now we have to save your parents. Don't run. Now, I know you're scared, but never run when you're scared. Rule 7. Please. [...]
DOCTOR 11: Rule one. The Doctor lies.

_{-- Let's Kill Hitler (New Who, Series 6)}

Twelfth Doctor

Rule #1: use your enemies' power against them.

CLARA: Rule number one of being the Doctor. Use your enemy's power against them.

_{-- Flatline (New Who, Series 8)}

Honourable mention

... for the golden rule Moffat invented to cover ALL Doctors, which is what defines him as the Doctor across all his regenerations: never cruel and never cowardly; never give up and never give in.

DOCTOR 11: Then what do I do?
CLARA: What you've always done. Be a Doctor. You told me the name you chose was a promise. What was the promise?
DOCTOR 10: Never cruel or cowardly.
DOCTOR 8.5: Never give up, never give in.

_{-- The Day of the Doctor (New Who, 50th anniversary special)}

Arguably the Doctor's final words to Clara could also be taken as a list of rules; I'll just stick that quote in here because it could count either as a list of Twelfth Doctor's Rules or simply as confirmation of the overarching rules I just mentioned.

DOCTOR: Run like hell, because you always need to. Laugh at everything, because it's always funny.
CLARA: No. Stop it. You're saying goodbye. Don't say goodbye!
DOCTOR: Never be cruel and never be cowardly. And if you ever are, always make amends.
CLARA: Stop it! Stop this. Stop it!
DOCTOR: Never eat pears. They're too squishy and they always make your chin wet. That one's quite important. Write it down.
CLARA: I didn't mean to do this. I'm sorry.
DOCTOR: It's okay. It's okay. I went too far. I broke all my own rules. I became the Hybrid. This is right. I accept it.

_{-- Hell Bent (New Who, Series 9)}

Answer 2

He also says 'First things first, but not necessarily in that order'. Not quite a Rule but definitely a Doctor-ism. Another one is 'Don't interfere in the affairs of other people/planets unless there are children crying'.