Cult Classic: The original sold very well, and it kept going for an extraordinarily long time (the developers continued to release updates until 2005). Another factor is the mod community, which was huge at its peak and has produced a lot of good stuff. People are still releasing stuff for the original OFP, though most of the community has shifted focus to the ARMA games..
Game Breaker: To a degree, the M1A1 Abrams tanks in Cold War Crisis - they're easily the strongest vehicles in the game and the Russian tanks can only compete through superior numbers. The campaign missions where you start in one are quite possibly the easiest in the game, and missions in Red Hammer tend to only use one of them at a time to even things out a little.
Minefields and attack helicopters are the only things that pose a really serious threat to an Abrams tank platoon, and you rarely come across either. There is only one minefield in the tank missions, and you're forewarned about it.
OFP also had numerous nukes. One pack included a biological warhead which would infect a soldier, and then any soldier they touched would get infected and so on. About 5 minutes after infection, the soldier dies. The first a player knows they are infected is when they die. An unreleased version had a bug where every object would get infected, so a player could be able to see the entire world diearound them: trees; shrubs; lampposts...
The Soviets speak with a very silly accent. Especially in the Red Hammer campaign, where some of them apparently inhaled helium.
That One Level: The main culprit is probably the mission "Alamo" in the original's Red Hammer expansion pack campaign: as an outline, the beginning of the mission is an Unexpected Gameplay Change, where the player is allowed to place defenses and ammo crates around a village (not that they're particularly important to the outcome) in an effort to defend the place from enemy tank attacks. There have been tears shed over this to say the least. It doesn't help that one of the easiest and most popular ways to finish the level is pretty bizarre, especially with regards to the game's usual tact for realism - it's possible to disable a powerful enemy tank at the start and use it to easily crush the rest of the attackers.