Although the music in the series is mostly pretty generic, the final boss battle in the first game is accompanied by some seriously epic battle music, complete with grandiose choir.
Demonic Spiders: Potentially any enemy in SOF2 on Consultant and Soldier of Fortune difficulties, due to the AI being a cheating bastard with accuracy (they have pixel-perfect aim at very long range, while you are screwed by recoil), visibility (they can see you through thick brush, smoke, and fog, and even behind hills), and grenade timing (sometimes they will telekinetically detonate it in midair).
"Funny Aneurysm" Moment: One of the levels has Saddam Hussein in it (he only appears in a cutscene), through cheats however, you can spawn and kill him. Now try to play this game now that Saddam is dead for real.
Narm: Most of the dialogue and voice-acting in Payback is so ridiculous and over-the-top that it's almost impossible to take seriously.
Some of the first game's death sounds and animations.
The Big Bad's death in the first game. Despite getting ripped in half by falling machinery, the only sound you hear is his death scream.
Nightmare Fuel: The slaughterhouse in the Sudan mission in the first game and the village of Pureza in the second game.
Sequelitis: The third game. No John Mullins, different developer, different story.
That One Boss: The final boss of the first game is regarded as this by many, with an extremely powerful weapon, nasty turret back-up and being absurdly resistant to everything with the Handwave of "he's wearing body armour".
The Interrogator in the Hong Kong prison in the second game, with his near-instant-death machine gun. And he's Made of Iron even though he doesn't wear armor.
The Final Boss in the second game is an attack chopper that rip you apart in seconds and takes an INSANE amount of ammo to bring down, this is the one time where the OICW actually comes in handy, as if you can adjust the range properly, you can lob grenades at it safely and defeat much faster then you would with the normal ammo.