Yes, it matters alot. Whether you choose a .com (general), com.au (Australia), or a .co.uk (United Kingdom)...etc depends alot on the location of the audience you are targeting. If you own a web design firm in UK and your domain is a .com and hosted in US, it is harder for people in UK to find you because search engines know where people are searching from and tends to give priority to websites that are hosted in their location. This is call this geo-targeting. In short, a well optimised .com.au website can rank well both in google.com (Google General) and google.com.au (Google Australia). A .com website may loose out to a .com.au website in google.com.au. Furthermore, many companies bought large number of good .com, .net ...etc doman names in order to sell them at a higher price - which makes it hard for you to get a good domain name. Though a country specific domain name can be more expensive, you often get better chances to choose a good domain name.
Depending on your budget, a .info, .biz or some funny extensions might be cheaper to register but harder to remember. A .com, .net or .org domain name seems to be more popular and easily remembered. If you are targeting at the international level or in United States and do not want to spend alot, go for .com, .net .org, .biz, .us or .info.