If you need online tool for this, you can try Yahoo pipes, but you have to toy with it for any single website and it is not very intuitive, in my opinion. Besides, getting the content to an e-reader friendly format is difficult even if you create the feed with full articles.
Calibre is cross-platform and it tries to automatically fetch the full articles from the rss. It does a relatively good job, even though it is not completely precise. However, you can customize the "recipe" for the website to suit your needs. I haven't done that, because I don't know the syntax it uses and have no time and desire to learn it. If you are like me, then you can probably aks for someone else to help you - there is such a tread at the Calibre forum. There are already many "recipes" preloaded with the program, so if the website of interest is a popular one, chances are, it is already there.
If you use Windows, you can get the rss2book program, which you can also find here at the forum. You can specify the content you want by using only regular expressions. It was my program of choice for getting full rss before, but since I switched to Linux, I abandoned it (it requires .NET). Other downsides, apart from being Windows-only, are that it has problems with accented characters and cyrillic is not supported. But if you are a Windows user and read only websites in English, this is the program for you.