Are there any bitcoin banks (online services) and what are the benefits and pitfalls of using them?
There are such services. But there's a good reason not to use them -- if one day the service is gone, so are all your Bitcoins. This has already happened once and will almost certainly happen again. As of yet, there are no companies I would consider sufficiently reputable in this business.

You can, however, keep both Bitcoins and other currencies in a TradeHill or Mt. Gox account. You can fairly easily transfer Bitcoins into and out of those accounts and they're run by well-financed companies that can reasonably be trusted. And both TradeHill and Mt. Gox have made noises about making their accounts more like online wallets.