I love newspaper databases for genealogy. The first, and in my opinion still the best, is "Early American Newspapers" part of genealogybank.com. I started using this at Harvard as a librarian when there was just Series 1 and now there are six series and I subscribe as an individual. I could get some of this database free as (1) a member of NEHGS or (2) via the Boston Public Library. However, I want the full magilla on this one.
The other newspaper databases that are out there include: (a) 19th Century Newspapers, which I get as a member of NEHGS. It's OK. There are a few tricks for searching, but it's not bad. However, their coverage is not as good as genealogybank.com for New England (my main research focus); (b) Newspaperarchive, which I recently let lapse. This is more for schools and universities than genealogists; and (c) Footnote.com. This is mostly recent stuff and not my thing.
I should say that I'm only talking about pre-1900 newspapers for the most part. Many people doing all-family genealogies will benefit from the databases of current newspapers which carry obituaries. Not my concern. I did that the old-fashioned way years ago--on a microfilm viewer at each local library.
My biggest gripe with these databases are their bogus sales gimmicks. Dates are not falsely advertised as such, but they are tricky. Some databases will boast newspapers from 1790 to 2010. Footnote does this. Then you go and try to search for this. On Footnote, the newspaper browse is by state and newspaper, and you can browse by time within those. I looked at each New England State and guess-what. Nothing before 1980. So where that 1790 number comes from is anyone's guess. So, there's one newspaper run that goes back that far. Ugh.
Another one is to say that a title run is 1870-1920 (like Newspaper Archive does) for the Lowell Sun, without telling you about the significant gaps in coverage (no newspapers in 1906 at all!). Ugh.
But it's worth it when you find this type of record.