I tend to find myself preferring champions with high mobility (Poppy, Evelynn, Singed etc) and I am interested in roaming. No point roaming with a slow champion. (I don't want a list of viable roamers, I roam with Poppy and she isn't recommended)
The move speed has to take into consideration:
- Base move speed
- (Short cooldown) Self move speed buff skills (e.g.Poppy, Zilean's and Nunu's self buffs)
- (Short cooldown) skills that increase mobility (e.g. Rammus' powerball)
- Exclude move speed items, including boots, phantom dancers etc.
Best Answer
FORMAT for the information below:
8 Second duration - 15 Second CD (starts on cast not on end of effect) so there are 7 seconds where you aren't being buffed (1 second if you have 40% cdr)
12 second duration 75 second cooldown. Sadism may best be used during a fight but using the ability to recover from an engagement while quickly moving to another lane shouldn't be underestimated.
Evelynn is a natural roamer with her invisibility. Also, the cooldown on her Dark Frenzy is reset whenever she gets a kill or assist. Last, the amount of time for her passive to kick in is the same as Boots of Mobility's passive.
Galio may deserve to be removed from this list as he is not truly a roamer but the ability buffs allies as well as him self and is only not active for 7 seconds at a time (12 second cooldown 5 second duration).
Raise Morale combined with Gangplank's ult can be a very potent combination regardless of allied team composition as it grants all nearby allies the move speed (and a damage) bonus while his ult slows fleeing enemies (or just pounds them if they decide to stay still).
Decisive Strike has an 8 Second cool down with a 3 second duration and Garen's Judgement removes and then reduces slows allowing him to gank more effectively.
See Janna's Zephyr ability above. The ability also has an active that slows the target.
Divine blessing has a cooldown of 10 seconds. If you have the mana, you can cast it over and over. Kayle also has an activateable move speed debuff slowing its target by 25% and dealing magic damage.
With a cooldown of 8 seconds and a duration of 4 seconds it would appear that Lightning Rush would significantly increase Kennen's mobility. However, this is only true if he has the opportunity to pass though enemies to recharge his energy as the ability costs 100.
Seismic Shard requires a target making it limited in its use as a "roaming" skill.
Master Yi is an excellent jungler/ganker/roamer with Alpha Strike, Highlander and the highest (tied with Pantheon and Nidalee in cougar form) base move speed (355) allowing him to initiate chase and escape quickly.
When you are between lanes as you roam you will get progressively faster (to the max of 70).
In Cougar form Nidalee can also pounce every three seconds at no cost increasing her mobility further.
Nocturne also benefits from a long ranged ult allowing him to gank from quite a distance allowing him to "roam" less but still have a presence.
Nunu is a good roamer and jungler. His Consume ability allows him to regain some of his lost health between ganks by using it one the monsters found in the jungle (or after a fight on the minions in the lane).
Poppy has increased movement speed and excellent tower diving capabilities granted by her ult.
Powerball can be activated to increase movement speed between lanes and initiate a fight as it pops up enemies he hits (though this ends the ability).
Rumble has a high base move speed and Scrap Shield has a cool down of 6 seconds.
Singed naturally benefits from high move speed has a high base move speed and his ult increases it further.
Teemo can be a good roamer as his increased movement speed allows him to switch lanes or scout the jungle areas quickly. During his excursions he can also drop mushrooms that will grant limited knowledge of where enemy champions are and prevent enemies from ganking/escaping (if they are silly enough to go into the bushes).
Trundle grants himself increased move speed and he can use Pillar of Filth slows enemy move speed and block terrain making him an effective roamer.
With a cooldown of 6 seconds there are only 2 seconds (at ability level 5) where Udyr is not increasing his movespeed (if you keep recasting bear stance).
Night Hunter has a range of 2000 allowing you to close on enemy champions from quite a distance fairly quickly. She also has tumble which allows her to chase even more effectively.
Warwick is a natural roamer/ganker with Blood Scent and his ult he can effectively initiate (in small fights) or pick off stragglers.
Zilean is best as support but can move quickly between lanes with Time Warp and Rewind. With some cooldown reduction and mana regeneration Zilean can cast Time Warp and Rewind over and over, sustaining the increased move speed.
Other Champions with abilities that grant increased movement without movespeed buffs include Aatrox, Caitlyn, Corki, Ezreal, Gragas, Graves, Irelia, Jarvan IV, Jax, Kassadin, Katarina, LeBlanc, Lee Sin, Maokai, Renekton, Shaco, Shen, Tristana, Tryndamere, Xin Zhao and Zac. Note these listed immediately prior are abilities that may require targets such as allied or enemy champions to function (examples being Katarina and Jax). Others like Caitlyn I list but her ability really isn't optimally used for movement as much as kiting and escaping.
Big list with lots of potential math to do to get the true fastest but I suspect the goal isn't to just be the fastest. Let me know if I missed something.
Edit: Information contained herein is compiled entirely from the two links provided in my comments to the original question.