With the v184.108.40.206 patch notes it is mentioned that Tryndamere had a bug where he couldn't use his ult during suppression. This sounded weird to me since I was under the idea that suppression was a stun that you couldn't cleanse out of or use abilities while suppressed. Looking around the Internet I can't seem to find a hard defined rule for when a champion may get out of this or use his ability, some champs can just do it with some abilities but I can't find a complete list. So which champion abilities can be used while suppressed?
Suppression a stun which you cannot cleanse out of. It is also unaffected by merc treads / any CC reductions, such as Irelia's passive. The only two ways to get out of it are either the caster gets interrupted or you use the active on quicksilver sash.
The suppression acts as a normal stun + locks all summoner spells (flash, cleanse)
The stun part of the suppression stops champions from using active skills (as of 16th Feb 2011), with the exceptions of:
Passive abilities will kick in, such as Anviva's egg.
It's important to note that Tryndamere's ult is the exception, not the rule, as it is one of the few (the only?) abilities that can be used during hard CC (Fear, Stun, Taunt, etc. Suppression counts as one of these).
I think it's important to note that Tryndamere's ult won't break the suppression, which will continue for its standard duration, but merely prevent him from dying (as normal). It's the same effect if you're in a regular stun.
In game terms, the only real way to get out of suppression is with the help of another champion -- namely, one with a forced movement ability. Janna's Maelstrom and Gragas' Barrel, as well as a few knockups, like Janna's tornado, will break the suppression.
Alternatively, silencing or otherwise interrupting the suppressor's channel works well too.
While this is the exception, there are ways some champions can cheat and out of suppression, and these are the champions with a built-in teleport, blink, or jump (Ezreal, Trista, Kassadin, to name a few).
Say a Warwick attempts to gank mid, and kill Tristana. If Tristana rocket jumps back to her tower exactly at the same time WW ults her, she will rocket jump away, and Warwick will teleport to where she jumped FROM. Trist will be suppressed, but will be jumping through the air for half the duration, and take no damage from the other half (as WW's attacks require melee range).
Note that of the three champions that have a suppress (Warwick, Malzahar, and Urgot) this is only super-effective against Warwick (as his requires melee range). It is effective against Malzahar if you get out of the range of his ult, and doesn't work against Urgot.