There are a whole bunch of good ones, and don't think you should watch the original first. A good abridged series does not require prior knowledge of the anime.
My favorites are:
Sailer moon, by moonsidesaturn. It's only two episodes, and it is never going to update again. But those two episodes are really great.
Avatar abridged, by Xanxibar. Hasn't updated in a while, but it's really funny. For this one I would recommend having seen the original. For it fully exploits any plots wholes, and is surprisingly true to the original characters.
All the work of hbi2k, all of them are very funny. (I haven't seen a single of the original episodes though)
One of the best abrigded series, but largely unknown is Lupin the Third by Kaiser Nekko. They are a bit hard to find because of problems with copyright issues, but they are definitly worth watching. Especially if you get all the references.
If you don't want to stick to anime alone, then I recommend SpoofTrailers: He/She/it mostly did Lord of the Ring spoofs (it's trying to cover the entire movie and is now at the beginning of movie 3). But he/she/it also has done some other funny work.
