While I am not opposed to paying for a service that gets me the records I need, I am also all for saving some bucks when I can. And the good news is, there are a whole host of free newspaper sites available for genealogists. Most of the free sites tend to be state-based newspaper projects hosted by a state archive, library, historical society, university, or some other interested state entity. There is also the Library of Congress’s Chronicling America which holds digitized newspapers and a directory of newspapers from all over the United States. So here is a list of some of my favorite, free, sites for finding or accessing newspapers online.
Directories and Lists of Newspapers:
- Chronicling America, from the Library of Congress, Historic American Newspapers; see also the US Newspaper Directory 1690-present
- The Ancestor Hunt – Newspaper Links
- BGSU LibGuide: Historical U.S. Newspapers Online – a guide to historical U.S. newspapers that are freely available on the Internet.
- Cyndi’s List – Newspapers
My Favorite Digitized Newspaper Sites (this is by no means an exhaustive list, it’s just a few of the sites I’ve used frequently and have found quite useful):
- Colorado Historic Newspapers Collection
- Wyoming Newspapers, from the Wyoming State Library
- Utah Digital Newspapers
- California Digital Newspaper Collection
- Fulton Search, an easier search engine to Old Fulton Postcards (newspapers)
- NYS Historic Newspapers (New York State)
- Washington Digital Newspapers
And I recently had the chance to do some research in New Zealand (online of course) and found this fantastic digitized newspaper site, Papers Past, that helped me find many answers and clues for the project I was working on.
Like I said, this is not an exhaustive list. When I find myself in a new area, I usually head over to one or more of the list sites mentioned first to find out what is available for that place in what time frames. There are so many small projects out there, small public libraries, universities small and large, museums, genealogical and historical societies, and so on that are digitizing their own collections as well. Be sure to do some looking around. You will be surprised by what you find!
Genealogy Pants 
It was not meant to be an exhaustive list and my personal research is not in Texas. I gave resources to find things like the Portal. There are way too many to list and many other sites have already done that, which are mentioned. But yes, the Portal is another great newspaper site.
This is a great list. I use many of the same sites in my talks on using newspapers for genealogy research.
Trove in Australia is great (all free) and in Canada, many provinces have older newspapers digitized and available for free. For instance, British Columbia:https://open.library.ubc.ca/collections/bcnewspapers