The dialog in Asterix relies heavily on puns and wordplay, the translation between French and English is actually quite good. The character names are changed into puns that are more appropriate for the English-speaking ear.

The main theme in Asterix is the adventures of him and his friend Obelix, the menhir deliverer upon whom the effects of the Magic Potion is permanent. Generally, there will be some kind of crisis or other event which require the attention of the intrepid Gaul pair and they will set off to go solve it. Other cultures have appeared, and the historical accuracy is generally... loose, to say the least. There are several historical events and locations they visit, and even some events that are attributed to the Gauls (for example, the nose of the Sphinx is broken off because Obelix was climbing on it).

Other recurring themes are the Pirates as AK mentioned, who often encounter and are summarily beaten by the Gauls (in later works, they will sometimes sink their own ship, thus denying the Gauls the pleasure of doing so. The captain often references his mounting debt at the hands of the Gauls after they have been sunk).

Another is the end-of-tale banquet, in which all Gauls are in attendance except the bard, Assurancetourix (Cacofonix in English) who is gagged and tied to a tree, lest his music disturb the atmosphere. It should be noted that in later parts of the series, the bard's music is so bad that he causes a torrential downpour, a gag initiated in Asterix and the Magic Carpet (written after the death of Goscinny) that was retained for the rest of the series.

Asterix is wildly popular in France, it has its own theme park (Parc Asterix) with several Asterix-themed rides and attractions. It's pretty fun, although probably more entertaining if you're a person who enjoys rides (of which I most certainly am not).

I've been a huge fan of this series since my childhood, if you want you can shoot me an email or an IM and I'll give you as much information as I can.