FORMAT for the information below:
Champion - Base Move Speed - Ability
or Abilities that grant additional
Blitzcrank - 325 - Overdrive grants
him (16 / 20 / 24 / 28 / 32)%
increased movement and (30 / 38 / 46 /
54 / 62)% attack speed for 8 seconds.
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)
Dr. Mundo - 345 - Sadism grants him
(15 / 25 / 35)% extra movement speed
for 12 seconds as well as heals him
for 40 / 55 / 70 % of his max health.
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 - 340 - Dark frenzy grants her A flat (4 / 8 / 12 / 16 / 20) movespeed bonus when she hits an enemy when any ability that stacks 4 times and lasts 3 seconds, and a ( 30 / 40 / 50 / 60 / 70)% movespeed bonus that removes slows and ignores unit collision for 3 seconds when activated
attack speed and (20 / 25 / 30)%
movement speed for 10 seconds.
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 - 335 - Righteous Gust creates
a directional draft for 5 seconds
which increasing the movement speed of
allies passing through it by (20 / 25
/ 30 / 35 / 40)%.
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).
Gangplank - 345 - Raise Morale grants
him (8 / 10 / 12 / 14 / 16) attack
damage and (3 / 4 / 5 / 6 / 7)%
movement speed passively. When
activated it grants Gangplank (14 /18
/22 /26 /30)% movement speed and (20
/28 /36 /44 /52) attack damage. Nearby
allies receive (7 /9 /11 /13 /15)%
movement speed and (10 /14 /18 /22
/26) attack damage.
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).
Garen - 340 - Decisive Strike grants
him (15 / 20 / 25 / 30 / 35)%
increased movement for 3 seconds.
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.
Hecarim - 345 -
Janna - 335 - Tailwind increases the
movement speed of all allied champions
by 3% while she's alive. Zephyr passively increases her movement speed by (8 /
10 / 12 / 14 / 16)% and enables her to
pass through units.
See Janna's Zephyr ability above. The ability also has an active that slows the target.
Kayle - 335 - Divine
Blessing increases an allied
champion's movement speed by 12% for
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.
Kennen - 335 - Lightning Rush grants
him a flat bonus to movement equal to
his base movement speed (after any
other bonuses are calculated) and the
ability to move through units for 4
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.
Malphite - 335 - Seismic
Shard steals (14 / 17 / 20 / 23 / 26)%
movement speed from the target for 4
Seismic Shard requires a target making it limited in its use as a "roaming" skill.
Yi - 355 - Highlander increases his
movespeed by 40% for 6/9/12 seconds.
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.
Miss Fortune - 325 - Strut grants
her an additional 25 movement speed
after not taking any damage for 7 or
more seconds, increasing each second
up to 70 maximum bonus speed.
When you are between lanes as you roam you will get progressively faster (to the max of 70).
Nidalee - 335 - Aspect of the
Cougar grants her 20 movement speed in
cougar form. Prowl grants 15% movement speed when moving through brush and for 2 seconds after she leaves it
In Cougar form Nidalee can also pounce every three seconds at no cost increasing her mobility further.
Nocturne - 345 - Duskbringer increases
his movespeed by (15 / 20 / 25 / 30 /
35)% while in the trail it or the
enemy champion leaves.
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 - 315 - Blood Boil grants an
allied unit (25 / 30 / 35 / 40 / 45)%
increased attack speed and (8 / 9 / 10 / 11 / 12)% increased movement
speed for 15 seconds. If cast on an
ally, Nunu also gains the effect of
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 - 320 - Paragon of
Demacia grants her (17 / 19 / 21 / 23
/ 25)% increased movement speed for 5
seconds when activated.
Poppy has increased movement speed and excellent tower diving capabilities granted by her ult.
Rammus - 310 - Powerball grants him
an increasing bonus to movement speed
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 - 320 - Scrap Shield grants
him (10 / 15 / 20 / 25 / 30)%
increased movement speed for 1 second.
When in the "Danger Zone" this amount
is increased by 30%.
Rumble has a high base move speed and Scrap Shield has a cool down of 6 seconds.
Singed - 320 - Insanity Potion grants him flat (35 / 50 / 65)
increased movement speed while active.
Singed naturally benefits from high move speed has a high base move speed and his ult increases it further.
Teemo - 305 - Move Quick increases
his movement speed by (10 / 14 / 18 /
22 / 26 )%. If Teemo gets hit by a
champion or turret while Moving Quick,
he gets knocked out of it. He can
activate it to gain double the
passive, for 3 seconds, which will not
be lost even if he is hit.
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 - 325 - Contaminate infects
a target location with his curse for 8
seconds, granting (20 / 35 / 50 / 65 /
80)% attack speed, (20 / 25 / 30 / 35
/ 40)% movement Speed, and (8 / 11 / 14 / 17 / 20)% healing and regenaration increase while on
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.
Udyr - 320 - Bear Stance grants him
(15 / 18 / 21 / 24 / 27)% increased
movement speed for (2 / 2.5 / 3 / 3.5
/ 4) seconds upon activation.
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).
Vayne - 310 - Night Hunter gains 40 Movement Speed when
moving towards an enemy champion.
After activating her ult, Final Hour, the bonus is tripled.
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 - 320 - Blood Scent senses
enemy champions under 50% life within
(1500 / 2300 / 3100 / 3900 / 4700)
distance of him; while he detects a
low-health enemy, he gains (20 / 25 /
30 / 35 / 40)% increased movement
Warwick is a natural roamer/ganker with Blood Scent and his ult he can effectively initiate (in small fights) or pick off stragglers.
Zilean - 310 - Time Warp increases
an allied champion's movement speed by
55% for (2.5 / 3.25 / 4 / 4.75 / 5.5)
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.