Original article by Ebrahim Saifuddin (HERE), simplified by IslamForKids.
*This list is taken from mainly from "Behashti Zewar (Heavenly Ornaments) [English - Urdu]" unless mentioned otherwise.
Acts Which Do Not Invalidate The Fast:
If a fasting person eats or drinks by accident (because they forgot they are fasting), then the fast will not break.
Even if they accidentally eat and drink a full-stomach, the fast will not break.
Even if they accidentally eats or drinks several times in the day, the fast will still not break.
A fly went down the throat, or some smoke or dust went down the throat on it's own,
Then the fast will not break.
However, if one did this intentionally, the fast will break.
A fibre (piece) of meat or a piece of betel-leaf, etc. was stuck in the teeth.
Because of cleaning the teeth (i.e. tooth brushing), this piece came out from in between the teeth and the person ate it.
However, he did not remove it from his mouth; It went down his throat on its own.
If this piece is less than the size of a gram-seed, the fast will not break.
If someone swallows their own saliva, the fast does not break (the amount swallowed doesn't matter).
After eating some betel-leaves, the person washed and gargled his mouth thoroughly.
Despite this, the redness of the saliva did not disappear.
There is no harm in this. The fast will still be valid.
Ghusl (bath) became compulsory at night.
However, the person did not have a bath and only took a bath during the day. The fast will be valid.
In fact, even if he does not bath the entire day, the fast will still be valid.
However, he will still be sinning for not bathing.
A person sniffed in a way that made the mucus of his nose go down his throat. His fast will not break.
Similarly, the fast does not break by sniffing and swallowing the saliva that is in the mouth.
A person vomitted unintentionally. The fast will not break, no matter the amount of vomit.
If he vomitted intentionally, his fast will still not break if the vomit was less than a full-mouth.
A small amount of vomit came out but it returned down the throat on its own. The fast will not break.
If a person puts water in his ears, the fast will not break.
Blood comes out from the mouth.
It is then swallowed together with saliva but the quantity of it was less than
of the saliva and its taste was not felt when it goes down the throat. The fast will not break.
If a person tastes something with his mouth and thereafter spits it out, the fast will not break.
However, it is makruh to do so unnecessarily.
But if one's husband is very hot-tempered and there is the fear that if the salt or water content in the gravy is not in order,
he will become extremely angry, it will be permissible to taste and will no longer be makruh.
It is makruh to soften any food with one's mouth and feed it to a child.
However, if this becomes necessary and there is no alternative, it will not be makruh.
Oxygen via oxygen masks do not invalidate the fast provided
if nothing but air is being delivered without any other particles. (Fatawa Usmani Vol.2 pg 180)
Backbiting although haram and a grave sin does not invalidate the fast. (Fatawa Rahimiyyah Vol.3 pg 123)