Ah, what a wonderful topic.
My favourite long-term character would be General Marcus, insane leader of the British Army.
He moved the British Army HQ to Exeter, after converting the Meterological Office into a military complex, and constantly has to fight off members of the Ethics Committee for Exeter (ECE), who usually attempt to find out how he's mistreating his men, to no avail. He tries incredibly hard to "arrange" the death of one Lieutenant Elston, one of his only competant men. The rank system in the army is a mess because of his unwillingness to give anybody ranks close to his. He has imprisoned all the other men in the army with the rank of "general" in the base's dungeon, which is filled with lethal levels of radiation. He arranges them to compete in fights to the death in the base's arena.
General Marcus started life off as an accountant before deciding to go off on holiday to Paris, whereupon his flight suffered technical difficulties. The next thing he knew he'd washed up on the Falklands. He was rescued by the British Navy who were blockading the isles at the time, and joined the army.
He is verbally affluent, despite his insanity, and doesn't actually do any work. He is obsessed with violence, and has his own political party, "The Military Dictatorship Party". He sees everyone as expendable, including the leader of the country, and is cowardly in direct battle. His battle plans are usually the worst, and most likely to get his men killed in the process. He actively attempts to impede the progress of his troops despite the fact he wishes to defeat the enemy, merely because he hates his men. He is patriotic to his country, and believes all other countries are his by right.
He is a fun character to write about as you can see.
My favourite short-term character, created for an exam, is called Gerald McFinnigan, the world's most boring man, and he was great fun to write about.