Eldar is the standard answer, but that's because it's the best Codex out there.
For the Imperium the main fast armies are White Scars (
SM), Space Wolves, Blood Angels and Ravenwing (
DA). Of those, it's generally accepted that Blood Angels are the weakest of the three and in tournaments are commonly taken as allies. They are also Melee focused which isn't what you're looking for. Space Wolves have it a bit better with Thunderwolf Cavalry, but they are combat focussed, so if that's not your style, stay well away, there isn't a lot to write about in the
SW codex aside
TWC.
Between
DA and
WS, Ravenwing have more firepower and more durablity. White Scars do however, have an extremely good build in Gladius (involving lots of free transports) and can pull bikes off reasonably well. They also have Hit and Run, which can allow them to get out of combat when they need to.
On the Xenos side of things, pretty much any army with the exception of Tau will suffice.
Orks can utilize fast vehicles and can have a Bike army which is extremely fast. They are however, melee orientated. While it is possible to make a shooty army with Orks, their strengths lie in combat. Additionally, they want large units, which can lend itself to deathstar builds.
Tyranids are Flying Monstrous Creatures which are exceptionally fast and have options to appear anywhere on the table courtesy of their Drop Pods. There is a misconception that they are close combat - they are not, they are close quarters. They want to shoot mainly and have the tools to do so. A major, major disadvantage is that one unit stands out above the rest and the Codex is known as Codex: Flyrants. Hopefully the rumoured book will resolve the internal balance, so if you go Tyranids, I would hold off on purchasing until the new dex.
Eldar and by extension Dark Eldar/Harlequins are the fastest armies in the game.
DE suffer from being melee focused and are outclassed by Craftworlds, who have better shooting and better movement. Harlequins outclass
DE in terms of combat.
DE work best when combined with the two armies to make the 'Freakshow', which attacks the leadership of the enemy rather than their toughness. Jimsolo has more information if you're interested in building such an army.
Necrons appear to be slow and in a way, they are. However, they have the durability to march up the field with ease, so it's not like you find yourself stuck in a part of the battlefield trying to wade across. That's not to say they are slow - several units such as Canoptek Wraiths, although melee focused, are extremely fast. In addition, they have the fastest transport in the game, bar none.
Hope this helps you out a bit