Right now just anyone who needs a website design/redesign. I'm not going local until next year.
'Anyone who needs a web site' isn't a target market. You're setting yourself up for the hardest marketing plan in the world. Pick a niche and market to that. It doesn't have to be local businesses; it could be a particular industry, or a client with a particular profile (e.g. based on age, personal situation, etc).
If you're targeting anyone with a pulse, you have no solid foundation for your marketing, you haven't a clue who your 'typical' customer may be (i.e. you don't have one) and you'll just end up wildly stabbing in the dark. You have to understand who you are marketing to, what their needs are, their day-to-day problems, what issues occur in their industries etc.
Is there any reason why you are not marketing locally until next year? Personally I found marketing locally the best way to build your business, particularly in the early stages. It's easier to get highly ranked in the search engines (e.g. Web Design City Name'), you can try local press and Directories, word of mouth, referrals, networking etc etc. Otherwise, you may find yourself just another number in the 6 million developers on Rentacoder or the ultra-competitive. price sensitive listings in sitepoint, where you are competing with guys from India and Eastern Europe who can afford to do web sites for $100.
Before anyone jumps on me, I'm not saying marketing locally is the only option, but I do think it's a great option when you first start out. You can also supplement it by targeting a more generic market if you feel the need - many suggest 80% to a niche, 20% to a generic.
Another way I've found of getting business is to become an expert in a particular software - for example, I know www.jshop.co.uk inside out, and regularly get people contacting me for bespoke modifications. Being a percieved expert is a great way to get high paying work, especially when it's a niche software (as opposed to OScommerce for examplem which probably has hundreds of thousands of people skilled in it to some degree).
Then of course are the usual ongoing tactics - article writing, plain and simple advertising (web sites, PPC, forums, magazines etc) and loads ofother things that no doubt other people will mention. But I do know from experience that targeting a niche will always be more productive than targeting 'anyone' - this is true in any industry.
I understand where you're coming from, I'm just doing a website for anyone right now to build up my portfolio, this is my first year in business. I am looking for niche's, right now my clients have mostly been sports and real estate websites.