Yes, there are a few different ways.
The simplest is using your mobile phone, connected by cable, infrared or (for newer stuff) bluetooth. It is quite slow on a conventional mobile (9.6kbps maybe?) so is only really suitable for plain text emails.
You can do something very similar with the new 3G phones, except the data rate is significantly better, roughly broadband but I can't remember exact numbers. The network coverage probably isn't widespread at the moment, but it's not bad and getting better as more networks bring it on line. You can also get 3G data cards that plug into your laptop to give you the aforementioned services, but they're likely to be more than you'd like to pay!
Lastly (for the moment!), you could try to use wifi hotspots. If you got a new laptop, it's likely that it'd come with wireless networking. More and more places are offering access points where you can log on to the internet wirelessly. They wouldn't be so widespread that you could rely solely on them, but they could work in conjunction with mobile phone access so that you could check your mails once a day and then pull up at a wifi hotspot once a week to read AnswerBank. Places that offer these include Starbucks, McDonalds, train stations, airports, hotels and more.