Can you connect to the internet on a DSi without using a connector?

The question is a bit unclear, you can only connect to the internet wirelessly, and you need a wi-fi network in range.

If you don't have a wireless router, you can:

• get a USB Nintendo Wi-Fi Connector (or similar device)
• use someone else's wireless network (in most cases this isn't allowed, and is probably passWord protected)
• Find a Wi-Fi Hotspot (Try public places like McDonalds)