The answer is no — not without taking special precautions. Now if you individually subscribe to an internet service (such as Comcast or FIOS) where you have your own modem and from that create a wireless network with a password, that is usually enough (unless you are super cautious and don’t do any personal business wirelessly).
Note that we are only discussing Wi-Fi wireless here — if your iPad has cellular data access, you can turn off your wireless and use your 3G (or 4G) network when you need some extra security.
There are solutions for wireless security, but the practical ones are not free. Essentially you contract with a service provider to encrypt your data, using something called a VPN (Virtual Private Network). Corporations use VPN’s all the time to keep communications to and from remote workers as secure as when they are in the office.
This article from MacWorld goes into more detail and suggests some companies that provide the VPN service. [Thanks to my brother Mike for the info and link.]
So if you want to surf safely from an open community wireless, or want to be safe when surfing from Starbucks, check out VPN’s-for-hire!