There are many different devices, with many different capabilities, and many different cellphone plans.
I use a T-Mobile Dash, which is a Windows Mobile 6 smartphone. It has a web browser, POP email client, and synchs with Outlook calendars. It has WiFi in addition to quad-band cellphone frequencies.
T-Mobile doesn't yet support cellphone data speeds that are fully adequate for web browsing, compared with DSL or cable modems. Other carriers may have more capabilities, at higher prices.