If you're just messing around, do not have a lot of money to open with or plan on doing frequent trading instead of buy and hold, go with Etrade, Datek or similar. Even if you use a full service broker, it is often handy to have an account with one of these guys just for putzing around because the transaction fees are cheap.
For full service, I like Schwab. They're on the cheaper side of the full service brokers and their online services are excellent. If you have at least $10K to open, there's no maintenance fees. If you have at least $100K, you qualify for their "Signature" service and you get all of their perks for free.
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