Depending on the site you choose to monitor, some of the following tools will work and some won't. The first tool is http://www.alexa.com/ it will give you all sorts of stats on a website including an estimate of popularity and estimates on demographics.
the Next tool is to do a google search on a website except include the phrase "site:" before you enter in the domain name. for example "site:http://www.internetmarket.com.au" will show all the sites indexed by google for that specific domain. Be careful though because "site:http://www.internetmarket.com.au" might give different results to "site:http://www.internetmarket.com.au".
http://www.similarweb.com/ also has a free search tool to give you marketeting information on a particular website, it is gives similar stats to alexa.com.
Google Trends found at https://www.google.com.au/trends/ can give you interesting information if you your in your competitions business name. The graph given on a Google Trends search is not the same as Google Adwords Keyword Tool. Google Trends measures how much 'interest' is for each search term and not how many searches are performed each month.
Next is Google Adwords ( https://www.google.com.au/adwords/ ) you do need to sign up for a Google Adwords account but you don't need to give your credit card information away. Google Adwords Keyword Tool is an excellent free service that will give you lots of information on search terms like your competitions business name.
Depending on your business https://www.yellowpages.com.au might be able to help. you can search for your industry name and look at your competitions listings.
http://www.whereis.com/ allows you to search for an industry or business name. This can give you a lot of information on the physical locations of your competition.
FaceBook Search ( https://www.facebook.com/srch.php ) might be able to help you find your competitions FaceBook page.
LinkedIn ( https://au.linkedin.com/ ) is also a great place to look for your competition, but some peoples profiles will know you have been looking. You can get all sorts of information if you know the names of the people you are looking for. LinkedIn is the world's largest professional network, it is also Australia's largest too.
YouTube is one of the largest websites on the internet so if their is a publicly available video produced by your competition then it is a good idea to look for it there. the website ( https://www.youtube.com/ ) also has shows stats on how many people view each video, this can be a good thing to note.
Finally... a standard Google & Bing search can bring up interesting information.