What brand of cell phones come with Internet access?

Pretty much all of them. I'm sure the list of cells that don't provide internet would be much shorter. You can also go the website of whatever cell provider you intend to go with and find out for yourself.

One question to ask yourself before you purchase a cell... Will you be using it more as a phone that has web capabilities, or more as a fully web-capable, highly portable mini-computer that happens to be a phone (like me)? I say this because if it's the former, any cheap POS will do. The latter and I say do not go cheap!!

Are you asking about brands of cell phones?

LG, Apple, Samsung, Rim, Palm, Nokia, Toshiba all make phones that can access the internet. There are a few that make phones without that capability.

Or brand of providers?

ATT, Verizon, T-mobile, Boost, cricket, Virgin etc..
http://www.phonedog.com/cell-phone-research/companies/
All providers seem to allow net access.

No-I have Tracfone- THAT brand doesn't have internet capacity. I asked the company.