incident noun 
an event which is either unpleasant or
unusual:an isolated/serious/unfortunate
incidentA youth was seriously injured in a
shooting incident on Saturday night.
accident noun
1 something
which happens unexpectedly and unintentionally, and which often damages
something or injures someone:
Josh had
an accident and spilled water all over his work.
She was injured in a car/road accident (= when one car hit another).
I've only dealt with the nouns here as otherwise there are too many options to discuss. These are definitions from www.dictionary.cambridge.org - this is the dictionary that I use with my students online. Notice the difference in meaning - accident more often refers to something that harms or injures, whereas incident can be any unpleasant event, possibly NOT harmful.
Kind regards
Ruth