1. Security / information theft
People who are wary of buying online frequently say that their main worry is that credit card information or other details that they provide in an online transaction will not be secure. Their concern is understandable, as the news media regularly carry stories of security breaches where people's sensitive information is at risk of exposure.
So what measures can you take to protect yourself?
First, buy only from reputable sellers (either directly or via a reputable auction or re-sale site). If you're not sure about a particular seller, you can check up on them by doing an online search. Your local trading standards office might also have some useful information (and you can find your local trading standards office by doing a post code search on the Trading Standards Institute website).
Online auction sites or sites where people sell used goods will usually have a seller rating and feedback system, which makes it easy to evaluate a prospective seller when you make purchases on those types of websites.
Second, pay attention to security. When entering credit card or other payment information, the web page address (shown in your browser bar) should begin with "https" rather than just "http", as the "s" indicates that information you send via the web page is encrypted. You should also look for the closed padlock symbol, which is usually at the bottom of your browser. If you click on the padlock, you should get information that confirms the identity of the seller. Note, however, that the padlock symbol can be counterfeited, so it's not in itself an absolute guarantee of security.
After the transaction, you should check your credit card statement (either online or when you get the printed copy in the post) to ensure that online purchases are as you expect them to be.
As with all online activity, protect your computer with good and up to date security, anti-virus and anti-spyware software.