As an ADC main with currently 73% win rate and ~4.3 KDA on Varus, I think that he's in a solid place. His playstyle vastly differs from other carries in that you really do want to have extremely careful positioning. And by extremely careful I mean that you'll probably be pissing off your teammates when they're all dead and you're alive. Dom yells at me all the time for how far back I am in teamfights, constantly going in and out of engagements to reassess the situation while utilizing his Q to poke down the enemies all at once until it's safe enough for me to be in a fully committed engagement.
Most people don't take into account Varus' passive. I find that it is most effective while taking down turrets and inhibitors, and I let my team know not to clear all of the enemy minions so that I can have a consistently higher attack speed while taking out a tower, swapping out every 3-5 hits to kill a minion to refresh his passive.
It's also incredibly useful in situations where you are duelling multiple people at once. It's happened on more than one occasion where I'm the last man standing and 1v3, while the three have already been poked down and torn up in a teamfight, sometimes it was his passive alone that won it for me.
If you think 20% attack speed is insignificant, I challenge you to start the game with that much attack speed from runes and masteries. That's a free Zeal you have for 3 seconds. Both the speed and duration are doubled when getting a champion kill or assist, 40% is equivalent to a stinger, and only 10% shy of a phantom dancer or zephyr.
If you're having trouble with his mobility, try building him movement speed. Take MS Quints, put 3 points into Fleet of Foot in utility, build him with 
(alacrity or furor), 
, 
, 
, 
, 
The best supports for Varus:
I have a specific mastery page for Varus if you'reinterested, as well as a specific runepage for him, though I also commonly use MSAD, AD Res, Hybrid, depending on their comp.
Personally, I feel like Varus over the time has fallen in a position from balanced to least favorable picks. As an immobile ADC currently he has the worst non-ult CC against chasing enemies, most of the time he has to use his ult which still has hugeass cooldown at lower ranks. His passive has atk speed values so miniscule that it hardly affects any outcome. His E has damage, slow and grievous wounds - a strong combination as it may seem, but no so after you take into consideration ridiculously high cd at lower ranks, aoe range, cast time. I'd like to see if Riot has any plans for him in the future.
