I pointed the link to Twitter's article about requirements for applying for Account Verification. It gives more information about the requirements for getting your account verified. Verification was previously only available to well known entities like celebrities or large brands. The article starts off with:

Submitting a request

To be able to complete the form, your account must have the following:

A verified phone number
A confirmed email address
A bio
A profile photo
A header photo
A birthday (for accounts that are not company, brand, or organization accounts)
A website
Tweets set as public in Tweet privacy settings

Actually, it's the account verification submission that is open to all, and not that everyone's account will be verified. :)

I got my account verified within hours using that form

From what I gather, with that information Twitter determines if you're a person of note? I expect some less active Twitter users might not get the response that rustybrick did ;)

Hi I checked the "brand" checkbox but I can't proceed futher, ie the next button doesn't work. Anyone else having probs with this setup? If you don't check the brand/company box.. it'll ask for birthday etc.

Again, i'll repeat what I said, it's the application that's open to all, and it's not a guarantee of acceptance.

If the form processes in real time and if it won't proceed it's likely the account doesn't meet the criterion set down by twitter.

I just signed up one of my Brand accounts for verification. No issues at all. It told me that I needed to verify a phone and e-mail, and then let me proceed through the process.

Twitter is crashing and burning into an anti free-speech haven .... the SA just depostied another 40950493805 dollars. Please keep NOT tracking the radicals.

nothing to see... move along.

Unless you have a billion followers, good luck. ;-)

Yeah I've seen accounts with thousands followers only that are verified..