To get a rough idea of how the competition is doing in terms of traffic to their website you could use the tools below. Beware, these tools can be wrong! Alexa and MetrixMarket are free.

Alexa
According to Alexa more then 10.000.000 people have downloaded their toolbar. By tracking the surf behavior of those who have the toolbar installed they are able to rank websites by traffic numbers. They do not estimate actual traffic numbers, just the traffic rank compared to other websites.
Type your an url in the textboxs below to see it's traffic. Go to their website to compare two websites to each other.

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MetrixMarket
Metrix estimates actual traffic numbers by looking at a sample of more then 2 million users according to the website. Their methodology is proprietary information and a 'closely guarded secret at this time'. They estimate the numbers to be within 5-15% of actual traffic figures, " although occasionally a site will fall outside that percentage".

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If you have a budget for this type of information you could consider HitWise or Nielsen/Netratings for more reliable data. Check out the DMOZ Statistics and Demographics category for more related links.

Where does your competitors traffic come from ?

The most obvious thing to do is check their incoming links, investigate which websites link to their website. Most search engines have a command for this, the syntax is usually link:http://www.example.com . The syntax or an option to search for links is usually indicated on the advanced search page. Google is known not to show all backward links so other engines are usually more suitable for this type of research. Try Alltheweb.com for more results.

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Some of your competitors may have public traffic counters on their site, such as those from eXTReMe or Nedstat Basic for example. These allow you to peek in the referrer logs of any site that uses their free tracking service. Searching for a combination of keywords related to your website combined with a unique fragment from the tracker codes will reveal these sites. The nedstat basic tracker for example has an image alt attribute that says "Nedstat Basic - Free website statistics". Searching for keywords nedstat basic on Google shows a number of sites about 'keywords' that will share their referral data with you.

Last but not least you'll want to know how they are doing in the major search engines. Ranking Analysis Software can help automate that task, but make sure you do proper keyword research first!