David Ganz writes:

Ron Ward writes:

Dave Ginsburg writes:

Making of America - Cornell
They have Harper's Monthly from June 1850 to May 1899.)
http://ebooks.library.cornell.edu/m/moa/browse.html

Making of America - University of Michigan
quod.lib.umich.edu/m/moajrnl/browse.journals/

Hunt's Merchants' Magazine at HathiTrust
Click on "Catalog Record" to find additional volumes. Sometimes the quality of the scan varies by university source and some sources have different volumes; one should check all source universities, if necessary.
babel.hathitrust.org/cgi/ls?field1=ocr;q1=hunt%27s%20merchants%27%20magazine;a=srchls;lmt=ft

Niles' Weekly Register at HathiTrust
(same advice as above)
babel.hathitrust.org/cgi/ls?field1=ocr;q1=Niles%27%20weekly%20register;a=srchls;lmt=ft

I'm sure that HathiTrust has a lot more periodicals than I've ever looked for. Finding them is sometimes a chore: for example, searching on "Niles' Register" didn't return the results that "Niles' Weekly Register" did. (I suppose it's barely possible that I'm as poor an Internet searcher as my wife, a trained researcher, claims.) Also, it's easy to download a .pdf file of an entire volume from Google Books, while one can only download .pdf files of individual pages from HathiTrust (and only 20 pages or so at a time).

By the way, the current Harper's Magazine website (http://harpers.org/) has all archives for Harper's Monthly going back to June 1850, which is available to current Harper's subscribers. I looked very briefly, but didn't find a good source for Harper's Weekly.

To read the earlier E-Sylum article, see:QUERY: ARE THERE ANY SEARCH SITES FOR OLD MAGAZINES?(www.coinbooks.org/esylum_v16n37a23.html)