1. Dreams
The jinn are able to affect the subconscious mind:
The good dream is from Allah and the evil dream is from the devil. If one sees a dream which one does not like, he should spit on his left side and take the refuge of Allah from the devil; it will not do him any harm, and he should not disclose it to anyone. If he sees a good dream he should feel pleased but should not disclose it to anyone but whom he loves. [Muslim]
2. Thoughts
They are also capable of affecting the conscious mind and introducing thoughts:
The devil comes to one of you and says: Who created this and that? till he questions: Who created your Lord? When he comes to that, one should seek refuge in Allah and keep away (from such thoughts). [Muslim]
3. Homes and food
The jinn may enter and occupy homes, and eat and drink from the food of its residents:
When a person enters his house and mentions the name of Allah at the time of entering it and while eating food, satan says (addressing himself): You have no place to spend the night and no evening meal; but when he enters without mentioning the name of Allah, satan says: You have found a place to spend the night. And when he does not mention the name of Allah while eating food, he (satan) says: You have found a place to spend the night and evening meal. [Muslim]
The wicked among them may also cause houses to burn through the agency of animals present in the house:
When you go to sleep, extinguish your lamps, for the devil may guide a creature like this [rat] to this [lamp] and cause you to burn. [Abu Dawud]
4. Birth
At birth, every child is prodded by a devil:
There is none born among the off-spring of Adam, but satan touches (pokes) it. A child therefore, cries loudly at the time of birth because of satan’s touch, except Mary and her child. [Al-Bukhari]
5. Sickness
Some physical human sicknesses are caused by the effects of the jinn:
The destruction of my nation (followers) will be [assassination by] stabbing and plague. The companions enquired saying: O Messenger of Allah, we understand stabbing but what is a plague? The Messenger of Allah (ﷺ) responded: [That is] the stabbing (harassment) from enemies among the jinn. [Death] by either way is martyrdom. [Ahmad]
It is one of the kicks of the devil [the Prophet answered in the case of a woman who complained about vaginal bleeding other than her menstrual period]. [Abu Dawud]
Zaynab, the wife of 'Abdullah ibn Mas'ud, told that 'Abdullah said: I heard the Messenger of Allah (ﷺ) saying: Spells, charms and love-potions are shirk (polytheism). I asked: Why do you say this? I swear by Allah, when my eye was twitching I used to go to so-and-so, the Jew, who applied a spell to it (i.e. the necklace around my neck). When he applied the spell to it, it calmed down. Abdullah said: That was just the work of the devil who was picking it with his hand, and when he uttered the spell on it, he desisted. All you need to do is to say as the Messenger of Allah (ﷺ) used to say: Remove the harm, O Lord of men, and heal. You are the Healer. There is no remedy but Your remedy which leaves no disease behind. [Abu Dawud]
6. Death
At the time of death, the devils try their utmost to cause the believers to go astray:
The Messenger of Allah (ﷺ) used to supplicate: O Allah, I take refuge with You from my house falling on me, I take refuge with You from falling into an abyss, I take refuge with You from drowning burning and decrepitude. I take refuge with You from the devil harming me at the time of my death, I take refuge with You from dying in Your path while retreating, and I take refuge with You from dying of the sting of a poisonous creature. [Abu Dawud]
7. Carnal relations
The majority of scholars affirm the possibility of humans and jinn having sexual relations. This is supported by the following citations in addition to actual incidents as reported by male & female victims and ruqat (practitioners of ruqyah treatment):
[Maidens of Paradise] whom no man or jinni before them has deflowered (55:74).
It may also be implied from the above verse that male jinn are able to deflower females similar to male humans.
At the time of intercourse, the Prophet advised couples to say: With the Name of Allah. O Allah, keep the devil away from us and keep him away from what You bestow upon us (i.e. children). [Al-Bukhari]
This is by no means an exhaustive list. The jinn interact with humans in more ways than listed in this post.