I have 2 Coverdell ESA accounts and 1 Roth IRA with TDAmeritrade, 1 Roth IRA with Vanguard, 1 IRA with Fidelity, and my trading account is with Interactive Brokers. Here's my thoughts on each:
TDAmeritrade has the ThinkOrSwim trading app which is great for a chart based trader like myself. It's really powerful, especially for options. There's plenty of options guys out there running millions of dollars and using TOS as their charting package. This probably doesn't apply to most people in this forum however. So I'll just say that TDA is fine for most people. They have quite a few commission free ETFs and the interface is fine. You can do options, currencies, commodities, all sorts of stuff with TDA but commissions are high if you are an active trader. TDA is about the only brokerage I found that could do Coverdell ESA college savings accounts.
Fidelity seems to have more research available along with lower commissions than TDA. I don't really use it for that, but it's probably great for most people.
Vanguard doesn't seem to give me much info, or at least it's difficult to find. I'd say that Vanguard is the most bare bones however they are also the cheapest. You can trade their Vanguard ETFs for free. If you are just gonna buy Vanguard index ETFs the cheapest way to do it is Vanguard. I should probably move my Fidelity and TDA IRAs over to Vanguard but I just haven't done it yet.
Interactive Brokers is really only for professional traders. They have very low commissions ($.005 a share), excellent execution and the lowest margin rates of anybody. They can handle most accounts. You can buy stocks in markets all over the world, currencies, commodities, German bunds, whatever the heck you want. You can short stocks with IB that most other brokers don't have. Most professional individual traders use IB. It's amazing how much more money I made switching from TDA to IB. I was paying way too much for commissions.
My recommendation for most people is Vanguard or Fidelity.