When writing a new website and choosing keywords, it's easy to make the mistake of choosing ones which are far too competitive. For a new website, it will be difficult to rank well for competitive keywords unless you can get some very high quality links from high PR sites.
Competitiveness is a difficult thing to measure and it has to be balanced against the search volume for any particular keywords. It might be worth optimising for competitive keywords if the search volume is very high and you don't mind taking a longer term view of ranking well. Taking the opposite view, it isn't worth optimising for uncompetitive keywords if the search volume is very low.
One way of investigating the competitiveness of keywords is by using Google's own keyword research tool at https://adwords.google.com/select/KeywordToolExternal. This tool shows monthly search volumes for keywords together with a rough gauge of the competition for the keywords.
Another rough way of gauging the competition is by using the allintitle: operator when doing a search. Using the allintitle operator makes the SERPS only contain those pages which have the search words in their title. Since a page title is a key SEO factor, the number of results returned is a rough and ready gauge of competitiveness. For example, if you want to measure the competition for web design, do the following search on google.co.uk:
This returns 9,800,000 results. Trying:
returns 13,800,000 results.
Contrast these numbers with a set of keywords that we can guess are pretty uncompetitive:
This returns 639 results, or ...
allintitle:web design worcester
which returns 1050 results.
Of course, the number of pages that include keywords in their title doesn't tell you the full story of how competitive a set of keywords are but it is a start. For one thing, allintitle doesn't tell you how well optimised the pages are, e.g. the first 50 pages in the results might have good links and content and be hard to beat without a lot of work. allintitle though is a useful tool to add to your SEO arsenal.