Sveriges Släktforskarförbund (The National Swedish Genealogical Society) reports that the Royal Library continues to grow its online newspaper collection with the ultimate goal of having 2 million pages from over 60 historic newspapers online by the end of 2017. This is a tremendous collection for those researching Swedish ancestors. The newspapers have been digitized and OCRed but keep in mind the OCR technology is far from perfect so even if you do not find your ancestor using “Search” a page-by-page review of a local newspaper may be necessary.
While the site is in Swedish, it is easy to use even if you don’t read Swedish. There are essentially two options. First, put your search terms in the big empty field in the middle of the page and press Sök (Search).
This will return hits from all newspapers-historic and modern. And if there are not too many you can read them all or at that point you can adjust the time period to limit the search.
The second option is to use the browse function “Bläddra Bland Dagstidningar” to narrow down which newspapers will be returned. 
You can click on the “+ Se fler” button to see the full list of newspapers. You merely click on the newspaper from the location you are researching and it returns the entire set of that newspaper that has been digitized. Than you either review, page-by-page, or Search in the newspaper.
Note there are 400 available newspapers (some are not viewable online, but most of the historic ones are.) The historic newspaper collection comprises the following.
TITLE FROM TO Arbetet 1887-08-06 1901-12-31 Barometern 1841-10-02 1895-12-31 Blekingsposten 1852-12-04 1884-12-09 Bollnäs tidning 1876-07-01 1880-05-01 Borås tidning 1838-12-07 1895-12-31 Carlscronas wekoblad 1764-01-21 1878-08-31 Carlscronas wekoblad 1753-12-29 1754-12-31 Carlscronas tidningar 1755-01-11 1764-01-14 Dagligt allehanda 1767-10-20 1849-02-12 Dalpilen 1854-01-02 1926-12-31 Eskilstunakuriren 1890-12-08 1900-12-31 Fahlu weckoblad 1786-09-16 1821-12-29 Falköpings tidning 1857-02-07 1896-12-30 Faluposten 1869-09-01 1890-12-27 Folkets röst 1849-10-06 1861-03-16 Gotlands tidning 1867-01-18 1888-01-07 Göteborgs handels- och sjöfartstidning 1832-03-22 1895-12-31 Göteborgs weckoblad 1875-01-02 1892-12-29 Göteborgsposten 1859-01-05 1895-12-31 Götheborgs allehanda 1774-01-01 1843-02-10 Götheborgs weckolista 1749-12-16 1758-12-20 Götheborgska nyheter 1765-01-05 1848-12-30 Härnösandsposten 1842-05-26 1895-12-31 Inrikes tidningar 1760-11-26 1820-12-29 Jönköpingsbladet 1843-11-25 1872-11-30 Jönköpingsposten 1865-01-17 1895-12-31 Kalmar 1864-07-30 1918-06-22 Karlshamns allehanda 1848-01-15 1895-12-31 Karlskrona weckoblad 1879-01-02 1895-12-31 Kristianstadsbladet 1856-09-20 1895-12-31 Lindesbergs allehanda 1876-01-07 1880-12-01 Lunds weckoblad 1775-01-05 1782-12-18 Lunds weckoblad 1813-01-02 1895-12-31 Malmö allehanda 1827-07-06 1893-01-31 Nerikes allehanda 1843-03-04 1895-12-31 Norden 1856-08-02 1861-12-07 Norra Skåne 1881-01-04 1897-12-06 Norrbottenskuriren 1861-12-14 1895-12-31 Norrbottensposten 1847-01-09 1895-12-31 Norrköpings tidningar 1787-01-03 1895-12-31 Norrköpings weckotidningar 1758-10-14 1786-12-30 Norrköpingskuriren 1858-10-02 1862-12-30 Norrlandsposten 1880-05-03 1880-12-31 Norrländska korrespondenten 1851-10-11 1873-12-16 Nya dagligt allehanda 1859-11-17 1895-12-31 Nya Wermlandstidningen 1851-01-02 1895-12-31 Nya Wexjöbladet 1846-12-11 1895-12-31 Nytt allvar och skämt 1843-01-19 1851-10-08 Nytt och gammalt 1783-01-03 1812-12-15 Post- och inrikes tidningar 1821-01-02 1895-12-31 Posttidningar 1645-01-02 1820-12-31 Reformatorn 1887-08-05 1965-03-28 Stockholms dagblad 1824-01-02 1895-12-31 Stockholmsposten 1778-10-29 1833-03-30 Sundsvalls tidning 1880-01-03 1895-12-31 Sundsvalls tidning Norrländska korrespondenten 1873-12-18 1879-12-30 Tidning för Wenersborgs stad och län 1848-12-12 1898-12-29 Umebladet 1847-09-25 1895-12-31 Upsala 1845-10-03 1895-12-31 Wermlands läns tidning 1871-12-27 1879-11-11 Wermlandstidningen 1842-12-21 1850-12-24 Wernamo tidning 1876-10-04 1884-12-19 Vestmanlands läns tidning 1831-02-10 1895-12-31 Wexjöbladet 1810-01-30 1855-09-24 Östergötlands veckoblad 1885-11-07 1895-11-08 Östgöta correspondenten 1838-09-24 1895-12-31 Östgötaposten 1895-11-15 1917-12-28