Without asking which terms they target - that is impossible. After all, how would someone find out what terms you are targetting with your SEO ? However, it is possible to find out which words/phrases send traffic to their sites. http://ci.trellian.com/ seems acceptable for most and is fairly cheap. http://www.hitwise.com is the gold standard - with applicable pricing.
I tought it is possible to find out with searching for the keywords which are most common in anchor text of links to the website. Thanks for the links, I'll check them, but I was thinking about free tool.
That would only give you the text in the links - not the terms the webmaster is optimising for. Link phrase is only one factor in SEO afterall. I doubt you would find a free tool for what you really need as it is rather expensive information to collate. The hitwise database is incredibly impressive as it is based on actual ISP server logs, not guestimates of traffic.
i don't believe this, if you post good content without spelling mistake, thats enough to get top of google page
Well you can' t know what kind of terms does your comperitors target, but you can see the keywords for which they tried to optimize their site (in which html elements, how many times, what is the most common term...). That kind of things do Tutor Seo Tool, you can check keyword cloud and keyword report with it.
i've a suggestion for you. search your competitor website in alexa.com. It will give you lot of keywords. take a look here - http://www.alexa.com/siteinfo/digitalpoint.com#
Only if your niche has very little or zero competition is this enough (unless you have incredibly viral-friendly content). WebDev
You can try several for example ahrefs has some free info or compete, there are several more if you dig around
http://www.opensiteexplorer.org/ is very powerful to check competition backlinks and keyword anchor text used for each link. I use it all the time.
You can use Tutor Spider Tool to find your competitors keywords. If you just register to http://tutor.rs/spider/ you can use spider tool for free, which means that you can create one project and to let spider to crawl ten pages for two main keywords of your competitors. But you can also add your own keywords (the one that you assume that your competitors used), not the one that spider have chosen.
check free competitor analysis as it is really helpful tool http://www.lxrmarketplace.com/seo-competitor-analysis-tool.html
just type your competitors url in backlinkwatch.com and find there targetted keywords in anchor text.
Go to Google adwards and select keyword planner from tools, click on 'search for new keyword and ad group ideas' from there type the URL of your competitor, from the result page select 'keyword ideas'. It will show all the relevant keywords used in that particular site or blog. Another way to spy your competitor keywords is: go to home of your competitor's website and click CTRL + U, this will show the whole source code, from there look for the major keywords used in website.
I'm surprised only one member mentioned Semrush and the rest were just giving inaccurate or impertinent replies. Semrush is a great tool for finding the keywords your competitors are optimising their sites for. You can also find out the search volume of their keywords, their current positions in Google for their keywords, their total traffic from search engines, how much traffic they get from different countries, etc. Another tool known as Compete (compete.com) has the same functions but Semrush is far better than it.