In an alternate universe, a Britannian prince and princess are exiled to Japan, where they become friends with the Prime Minister's son. When their home country invades and renames it Area Eleven, they fake their deaths and go into hiding.

Seven years later, the prince, named Lelouch, encounters a strange green-haired girl who gives him the power of Geass. Using this power, he becomes the masked terrorist Zero, setting in motion a rebellion that will eventually embroil the entire world in chaos!

... that's the basic premise, anyway. It also involves lots of mecha fighting, funny school council hijinks (he and his sister are pretending to be ordinary high school students), angst (his friend Suzaku is fighting for the Britannian army, not to mention most of his friends are Britannian students), drama, fanservice, xanatos roulettes galore, chess-master shenanigans, witches that like pizza, product placement, and a copious amount of Large Ham-ing.

All in all, it's a pretty fun show. It manages to be funny, bad-ass, and heartstring-tugging all at the same time. Some of the plotlines and mysteries have a little too much build-up for their conclusions, and there's some haxing of the characters and their mecha (Kallen and Suzaku, most notably). Just suspend your awareness of logic and disbelief, and you'll enjoy it fine.

Fans/critics tend to complain about how the series went downhill in the second season (often attributed to the fact that the original plans for R2 were scrapped), but while it's true that R2 suffered a lot from pacing issues and plot-holes that weren't present in the first season, not to mention some bad animation, the first season wasn't exactly perfect either. Code Geass was never very logical or believable, but it's fun and crazy enough that most of the time it's easy not to care.

The characters are largely sympathetic, and the show manages to portray no one as an absolute villain or hero. It's all about grey and grey morality, and though often the main protagonists (Lelouch and Suzaku, especially) stray into hypocrisy, they manage to be sympathetic and interesting nonetheless.

So yeah, it's a trainwreck, but it's a pretty darn fabulous one. Watch it for the characters and their relationships, the crack, the mecha battles, and the drama, not literary value.