One of my friends passed this web site to me - it is Newspaper Abstracts from a variety of newspapers published since 1704. These abstracts are all user-submitted, so they are not comprehensive in nature, nor do they cover every newspaper or every year of every newspaper. The site states:
Newspaper Abstracts goal is to become your complete resource for family history research using newspapers. Our site continues to grow with an average of over 600 new items added each month and currently contains over 26131 abstracts and extracts from historical newspapers. These articles range in size from a single entry to an entire newspaper issue, all provided by site visitors and made available to you free of charge.
If you click on the "United States" link on the web page, you can then search all of the US newspaper abstracts available.
There is a Search box on the left hand side of the page. Enter a surname in the box and click on [Search]. A list of newspaper abstracts will show on a new web page. Click on the newspaper title for a given entry and you will see the abstract of the item. The quickest way to search for your surname in the abstract is to do an [Edit] [Find] and insert the surname in the [Find] box that shows.
While this is not complete (but what newspaper archive is?) it is FREE and it can be useful. I found several new pieces of information in the 144 hits for my Seaver surname study.