Definitely
Cowboy Bebop if you want a dub. It's probably the only anime dub I can stomach. I almost even prefer it to the original cast it's so good, and that pretty much never happens. And it's a fantastic show in its own right, with probably the greatest TV soundtrack ever put together. I mean that seriously.
Berserk is one of my all-time favorites, but it's not light and easy. It's heavy, it's dark, it's emotionally crushing, and it's violent as hell. And the English dub sucks. It's still amazing, though, and worthy of being watched. I have 32 volumes of the manga in Japanese waiting for me to get skilled enough to read them with consistency.
I recently watched
Spice and Wolf, which was surprising. I had listened to some of the music and it was so good I wanted to see what the show was like. Figured I'd watch one episode and be done since it seems like it's going to be a ridiculous catgirl anime (or wolf, in this case), and it sort of flirts with that a little at times... but it's basically really political and all about business, the value and exchange of currency, and human greed, set in some sort of medieval kingdom. A guy basically hooks up with a wolf-deity that had been watching over a town that no longer appreciates her, and she wants to get back to her true home in the north, so she travels with him and they go through a lot of political and business intrigue as they go. It sounds ridiculous, and it's a weird concept, but it actually turned out to be quite compelling. And the art and music are gorgeous, which doesn't hurt.
The opening gives a pretty good idea. It's a little dark at times, but it isn't super heavy, and there's a lot of humor. No idea about the dub since I generally don't even bother with them.
I'd recommend
Akagi, an anime entirely about mahjong, but there's no English release, so fansub-only, and it's also quite dark. Effing crazy, though. I recommend it.