I think there is a flaw in your question – do you mean major papers, or all papers?
I used to have a job where I had to mail things to newspapers, and I found that most cities had at least one of each (Journal/Record/Post/Times/Register/etc.), but that many would have smaller circulations.
For example, the big paper in the big city near you might be the Springfield Record, with a daily circ of 90k, but there’s probably the smaller Springfield Post-Herald with a daily circ of 15k, and the weekly Springfield Shopper with a circ of 4k.
And the definition of ‘Major’ papers is fuzzy as well: there is a Washington Post, which gets about a million readers daily, and the Washington Times, which gets about 100k. 100k is still a pretty big newspaper, but it’s not thought of being as massive as the Post.
Historically most cities had 2 major papers, but for various reasons, (not the least of which is the expansion of Gannett, which uses Walmart-style tactics to crush smaller papers.) this is not the case any more.
For what it’s worth…
Among the top 100 newspapers by circulation, there are:
19 News (4 of which are Daily News)
12 Journal
10 Times
10 Post
8 Tribune
6 Star
6 Herald
5 Sentinel
5 Press
3 Gazette
3 Dispatch
3 Review
3 Sun
3 Union
2 Chronicle
2 Bee
2 Register
2 Telegram
2 Observer
1 Globe
1 Blade
1 Advertiser
etc…
The list I used is here:
http://www.accessabc.com/reader/top100.htm
and remember that this includes compound names like the Seattle Post-Intelligencer, and that some papers team up for Sunday papers, which gives them a higher circulation than they’d get the rest of the week.