What is the best way to download online magazine/newspaper articles?

You might find some helpful ideas in http://ask.metafilter.com/57613/Help-me-read-magazines-online-more-comfortably thread. You can also use Screengrab, an extension for Firefox, that allows you to save webpages.

There's also a Greasemonkey script that allows you to click on any NYT, WaPo, or LAT article and it automatically takes you to the printer friendly page. That way you don't have to click "next page" over and over when you're in the middle of reading an article. Maybe someone can help me out with a link for you.

I'm pretty sure this isn't what you are looking for... However, if you're looking for a way to get access to copyrighted and/or stuff you're supposed to pay for for free, that's not really what AskMe is for. That said, there are ways to access this sort of thing without paying for it by going to your (hopefully) local library. In many cases, periodicals like the Economist are available via full-text from databases your library may subscribe to. So, for one example, one of the libraries I have a card at has access to the Business and Company Resource Center database which is a Gale database. If I log in with my library card, I can use the advanced search feature to search only articles from the Economist (US or UK I think). Leaving the search box blank I can get all articles from each issue of the Economist, perfectly formatted with no ads. With the interface that my library has, I can then get a list of all the articles individually and I can opt to read them on screen, and/or email them to myself. Once they're in your email, as text, they're keyword searchable. With gmail, which is what I use they're speedily keyword searchable and you can filter them all into one folder for easier retrieval. I'm sure there are ways to automate this process that are 1) outside my range of expertise and 2) probably against licensing terms for these databases, but I bet some other crafy library patron or librarian could figure them out using some "check all boxes on this list" plug in and a few other simple tools.

I'm sorry I think I misunderstood your question which indicates that you already have access to these periodicals. I also wanted to mention that if you do have access to some of these databases (Expanded Academic ASAP is the one I am looking at now) you can create an RSS feed of all the new content in a particular journal feed which, in this case, can include headlines for every Economist article. If you pick and choose which ones you want to read, this can be a great way to click through to the articles you want while still getting a table of contents for each issue. Again I'm aware this may not be exactly what you're looking for, but if you click through the RSS feed [or automate a way to do it] you get, again, ad-free Economist with just a little finagling. I'd love to see someone automate this even further.

In Firefox, you could try using the "Work Offline" mode, to view the cached page: Offline mode allows you to view web pages you've previously visited without being connected to the Internet. Search the page titles and dates by bringing up History. (But not a full text search.) With IE or Firefox you could save the pages to disk with or without graphics. You could save the pages, and index them. http://www.microsoft.com/windows/products/winfamily/desktopsearch/default.mspx can index html files, and other document types. It looks like you can index pdf files with an add-on from Adobe called http://download.adobe.com/pub/adobe/acrobat/win/all/ifilter60.exe http://desktop.google.com/ has its own search feature. There are programs that copy entire sites, so that you can read them offline. An example - http://www.httrack.com/ , also look at ProxyTrack to build up an archive that you can access later on.

Just for clarification, the articles I want I can currently access but want to be able to get back to them in the future even if I no longer can access them later (economist articles stop being freely accessible after a few months).

Also: Both Google Notebook and Scrapbook let you search through what you've saved quite easily. I find that searching in GN is faster for large amounts of text/items though.