There are several ways in which you can check the current version of your wordpress installation. In the below methods "x.x.x" will actually indicate the version, in my case it shows 3.7.2.
I find this to be the easiest way to determine the current version of wordpress installation. There is a "readme.html" file located in the root directory of your wordpress installation. You can access this file in any browser to see the current version.
If your site blog is at "http://www.example.com", then you can access the readme at "http://www.example.com/readme.html"
If your site blog is at "http://blog.example.com", then you can access the readme at "http://blog.example.com/readme.html"
If your site blog is at "http://www.example.com/blog", then you can access the readme at "http://www.example.com/blog/readme.html"
Login to your wordpress dashboard and you can see the current version. Where in dashboard may vary depending on the version. It is best to use the browser search function(Ctrl+F) and search for "ver" to quickly find the version information.
In the blog I have, it is displayed under "Right Now" section. It says "You are using Wordpress x.x.x" with a button "Update to x.x.x".
Some people say the current version is displayed at the bottom in the dashboard page. For me it shows only "Get Version x.x.x" in the bottom with no information of current version. So it may be version dependent or it may display the current version only when you have the latest installed.
There is a "version.php" file in the "wp-includes" directory of your wordpress installation which has the version information. Accessing this file from browser is useless as it has no html output. You will not get any information from version.php when you access it from browser.
Explore your hosting files using your host interface or ftp client and open/edit "version.php" file. In the beginning lines of the file, you will find a line "$wp_version='x.x.x';". This number is your current version.
Go to any page or post on your blog and view source. In the source, look or search(search "generator")for the below line which tells you the current version.
<meta name="generator" content="WordPress x.x.x" />
View source works if you did not disable right click on your blog. How you access it depends on the browser you are using. In chrome, right click and select "view page source". In internet explorer right click and select "view source".
Hope that helps