You have many synergies with other champions in the game. Here are some that I personally think work well.
If you use your ultimate, Shen can use his ultimate on you, and the enemy team won't see either of you coming. I think there was a video on the top of r/leagueoflegends demonstrating how effective Shengar is. He can tank for you, and if he Vorpal Blades a champion, your burst on said target will heal you for a good amount of health. If he gets a taunt off on someone, go to work on them with your abilities.
Just like you may have seen during the LCS with a Twitch, Orianna can put her ball on Rengar, and perform a stealth ult that takes the enemy by surprise. Twitch can also do this, but Rengar is tankier than twitch so it works better on him. Orianna is a very useful utility mage, she can shield you for a huge amount with a free Armor and MR steriod. She can also haste you which is very useful for you. The haste can help you catch up to someone to root them.
Zil can give you 55% movement speed, and that is very useful if you're going for a kill with your ultimate. He can also revive you with his ultimate, and save you from losing a bonetooth stack. 55% speed is so huge, and at rank five it is a 5.5 second speed boost. This makes is very easy for you to get your E off on someone.
Renekton has an on demand stun, as well as an armor shred. If you want to do double bruiser bot lane, or you end up on the same team as him, Renekton is a fantastic partner to have. He lands a stun on someone, and you leap in, root them, and go to work. Double bruiser bot will crush any support/adc bot lane. Start fort pot if you're going double bruiser bot.
Nocturne and Rengar have good synergy. Nocturne's ult conceals the enemy vision, including pink wards, and your ult gives vision for him to dash into the battlefield with you, a terrifying combination if you're on the other team. If his fear tether reaches fruition, that can give you time to use your CC on the feared target.
You and TF can pull off some crazy assassinations, if you both use your ultimate. TF can stun someone up for you to kill with your empowered Q and other abilities. If you're on a team with TF AND Nocturne, the possibilities are endless. I can only imagine being on the other team getting triple ganked by Rengar, TF and Nocturne.
Although you don't see Teemo played that often nowadays... He can blind an enemy which is huge for duels. If he has a Riley's his slows can help you catch up to the enemy. If one of his mushrooms happen to catch someone in the jungle trying to get away, well. Let's just say they won't be getting away.
If you and Shaco show up from stealth on an unsuspecting ADC farming is almost a guaranteed kill. Both of you have very high assassination power. If he is your jungler, ask for an early gank top. He almost always has red buff before level 3, and he is one of the most slippery champions in the game. If one of his jack in the boxes fear someone trying to counterjungle, you can race in and get the kill.
Her traps reduce Armor and MR for a good amount of time, as well as revealing. Rengar can utilize this well because he is very mobile, to catch the enemy trail for a kill. If she chunks someone with a spear that will make your job as an assassin much easier. Also, she can give you a potent heal that gives Attack Speed, making you do work on enemy towers.
The same applies to Caitlyn traps, they don't reduce armor and MR but they do stun for a second or so. As an ADC, you need to be providing peel for her with your bolas. Make sure to kill anyone trying to attack her. If you can't get off that last bit of damage onto someone, her ultimate can clean them up.
Although Zix is your rival if you end up on the same team you two can make a disgustingly strong assasination combo. Once you both get Last Whisper there are few champions who can deal with both of your damage. Duo stealth can confuse people as well. Both of you have stealth capabilities and leaping capabilities. The single target damage output that comes from both of you is massive. Even if the enemy has armor.
Xin reduces his target's armor for free, which can make getting a kill much easier for you. Watch for him to initiate. In a fight, focus on who he has challenged, because you will do more damage to them. If you get a Xin gank, you're lucky, they are very potent. Chain CC the enemy to make it easy for him to get his knockup and slow. He is fantastic to add to your team comp.