Or, are they scam sites?
(I answered a similar question before.)
Essentially, you shouldn't trust a site you find on the Internet merely because it looks professional and real. Before signing up with any new service provider you found online, you should verify the authenticity of both the organization itself and their web site address. Even if the name displayed by a web site represents a legitimate brokerage firm, any site you happen to come across on the Internet could be an elaborate spoof of a real company, intended to capture your personal details (or worse).
First, to check if a brokerage firm is in fact registered to trade securities – in the United States – you can consult FINRA's BrokerCheck online service. This might be the first of many checks you should undertake ... after you convince yourself that FINRA is legitimate. A meta-problem ;-)
Then, if you want to know if the web site address is authentic, one way is to contact that broker offline using the contact information found from a trusted source, such as the FINRA BrokerCheck details. Unfortunately, those details do not currently appear to contain the broker's web site URL. (Else, that could be useful.)
Another thing to look at is the site's login or sign-up page, for a valid SSL certificate that is both issued to the correct legal name of the brokerage firm as well as has been signed by a well-known certificate authority (e.g. VeriSign).
For a financial services firm of any kind, you should look for and expect to see an Extended Validation Certificate. Any other kind of certificate might only assert that the certificate was issued to the domain-name owner, and not necessarily to an organization with the registered legal name. (Yes, anybody can register a domain with a similar name and then acquire a basic SSL certificate for that domain.)
FWIW, Scottrade and ShareBuilder are both legitimate brokers (I was aware already of each, but I also just checked in the FINRA tool), and the URLs currently linked to by the question are legitimate web site addresses for each. Also, you can see their EV certificates in action on secured pages here and here.
As to whether your investments with those brokers would be "safe" in the event of the broker failing (e.g. goes bankrupt), you'll want to know that they are members of the Securities Investor Protection Corporation (Wikipedia). (Of course, this kind of protection doesn't protect you if your investments simply go down in value.)
But do your own due diligence – always.
Both Scottrade and ING Direct (CapitalOne) have physical branches. Scottrade are wide-spread, ING/CapitalOne are less common (in California where I live, I have a bunch of Scottrade branches around where I live, but the only ING presence I know of is in LA on Sepulveda at Santa Monica).
So one way to verify the company is legit is to go to their physical location and talk to the people there. Similarly, you can find physical locations in major metropolitan areas for many other web-based discount brokers. In my area (SF Bay Area) we have Scottrade, ETrade, Fidelity, TD Ameritrade, and that's just those I've actually seen with my own eyes. You can just walk in and talk to the people there about their options and their web operations. It is hard and unlikely for a sting operation to set up a web of brick-and-mortar offices across the nation. Even Madoff had only one or two offices.
Of course I totally agree with Chris's answer, especially with regards to the SSL certificates' verification and spoofing and phishing avoidance.
How you check if a broker is legitimate:
1) Are they a registered broker dealer? Broker dealers have to be registered with FINRA and the SEC , which have their own databases for you to look up individuals and companies.
here is FINRA's http://www.finra.org/Investors/ToolsCalculators/BrokerCheck/
FINRA is a self-regulatory agency, the SEC is a federal government agency. All things considered, they pretty much have similar legislative authority over the industry. But thats a different story.
If the broker isn't able to produce information that would confirm their registration status, or if you can't readily find it in the regulators database, then that is a major red flag. The biggest red flag of them all.
2) If brokers are also acting as a consumer bank, such as how Merrill Lynch is now part of Bank of America and the accounts can be linked pretty easily, then they should will also be regulated by the FDIC. This means that you will be able to find the capital ratio that the company has, letting you know how stable it is as an institution.
Physical locations, the name, and duration of existence, or their rating on BBB have nothing to do with it.