Working in local history, I spend a lot of face to face time with our microfilm machine. We have reels for papers as far back as the mid-1800s, and there's no decade in the 20th century I haven't spent weeks in, looking for obituaries and specific articles. This is an absorbing experience, one which makes the past more personable: my mind is taking in the same material as readers decades before me, though in a different form. While the basic experience doesn't change, the kinds of things newspapers report on has.
In contemporary papers, social reporting is limited to wedding announcements -- but in older papers, even tea parties register entries.
2. Serial Stories
Readers may be aware that a lot of "novels" were originally published as newspaper or magazine serials. A lot of authors like Dickens and Asimov got their starts writing serialized novels or short stories for literary magazines.
I don't know if cities in Europe with train service still carry timetables, or if the internet has taken over the role. These are a treasure for realizing how dominant trains once were, though. (Steam boats were still offering twice-weekly passage from Selma in 1906: the Nettie Quill upriver to Montgomery and the Queen Mary downriver to Mobile.)
Care for a tren ride down to old Mexico?
4, Radio logs
When I first started visiting radio websites in the early 2000s, I thought finding lists of the music played during a given hour was an innovation. Nope -- that was being done in the 1930s, by my local paper.
5. World News
When I first began looking through the local newspapers of 1906, attempting to establish when my hometown trolley system ended service (1926), I discovered that local news was buried within the pages, with national and global news taking priority. This continued at least through the 1970s. There are even weekly quizzes to see how many news stories from around the world the reader recognizes -- as he ought, if he is a daily reader of the paper. Today, national news rarely appears, except in the case of disasters and presidential elections; radio, television, and the internet provide all of the general news, and the newspaper is left to fill a local niche. Opinion pieces on the news still provide a glimpse of what's going on outside, however.
Take a look at this political cartoon of FDR. By 1940 it was known that Roosevelt was partially paralyzed, but the cartoonist doesn't dwell on it. These days, every detail about people's personal lives becomes a national obsession if they become newsworthy.
7. Girls Only
Look at that, ladies, your very own page!
8. Personal Ads
Perhaps the oddest consistency in the papers I've surveyed is that until the 1970s or so, they feature -- on a daily basis -- tidbits from the news thirty years ago. (Except the one I discovered below, which was thirty-one years ago.)
10. The use of "solons" to refer to legislators