Recently James Corbett did an episode of Corbett Report on tools for online researchers. He listed some he uses and then his site members listed more in the comments.
Here I've compiled them all together with a brief explanation. You can now find this list on the links page in it's own "Tools" section. Suggestions for additions to the list are welcome, here in the comments, or sent to modmail anytime.
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youtube-dl - comprehensive program for downloading youtube videos - terminal or GUI - with many options
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Yandex Image Search - excellent image search & reverse image search too
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convertcase - convert the case of copy/pasted text
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highlighter - extension for an online highlighter
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HTtrack or webhttrack - download and preserve entire websites
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Web to PDF - online webpage to pdf convertor
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Million Short - Million Short makes it easy to discover sites that just don't make it to the top of the search engine results for whatever reason
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Archive web pages: https://archive.ph/ or https://archive.is
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https://ricks-apps.com/osx/sitesucker/ (like Htrack for OSX)
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nsfwyoutube.com - watch age-restriced videos on youtube without signing in. Just paste nsfw in front of youtube in addressbar of video
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Bypass Paywalls - extension for Chrome, Brave, Chromium - also available for Firefox
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Open Broadcaster Software - download in-progress live streamed videos
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ArchiveBox - powerful, self-hosted internet archiving solution to collect, save, and view sites you want to preserve offline
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Wallabag - self hostable application for saving web pages: Save and classify articles. Read them later. Freely.
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Keepnote - note taking application that works on Windows, Linux, and MacOS X
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WayBack Machine Downloader - Download archived webpages from wayback machine
An important thing to keep in mind:
Sometimes, to truly get to the bottom of things, you need to repeat the SAME exact search keyword search in MULTIPLE search engines (because they have different coverage/indexes) AND then do multiple variations (synonyms) of your keywords (again to all search engines), so that you get maximum coverage of information. Tedious, but very very useful at times.
WolframAlpha : a math , chemistry and physics computational engine. You can do chemical reactions, see radioactive isotope breakdowsn, do symbolic math solving, etc. Great for doing more complex calcs quickly https://www.wolframalpha.com/
BookFinder - the best used (and new) books search. Yeah, books. Those antique "things" that contain a lot of distilled information (I have a few thousand myself): https://www.bookfinder.com/
ResearchGate - sometimes you can find academic papers you can't download elsewhere (not even on sci-hub) here. Esp. non-peer-reviewed and from more obscure journals. https://www.researchgate.net/
Academia.edu - as ResearchGate, although you can't always download (depends on your academic/organization affiliations), but at least you can find papers, researchers and often read abstracts. https://www.academia.edu/
BASE - Universität Bielefeld Search - Academic search with high granularity and indexing also non-English papers. https://www.base-search.net/Search/Advanced
CORE - Search of Open Access research papers. https://core.ac.uk/search?q=%22
SemanticScholar - Another academic peer review paper search but with date range, academic field, author, journal and PDF filters. https://www.refseek.com/documents?q=
Science.Gov - Find out what the US Federal Agencies do in the name of science. Reports, papers, guidelines, etc. Very, very useful to find out what Federal science agencies are thinking/publishing. https://www.science.gov/scigov/desktop/en/search.html
DeepDyve - a meta-search engine for peer-reviewed, preprint and other papers (has also it's own chromium plugin that interfaces with PubMed and Google Scholar). https://www.deepdyve.com/search?query=
Publish or Perish - Best Desktop search tool for all for-paid scientific publications / peer review articles via CrossRef , Google Scholar , PubMed , Microsoft Academic , Scopus , Web of Science (you have to install API keys or have institution access for some of these). You get boolean searches, phrase searches, h-index , g-index ranking, sorting by date, citations, etc. The best tool for serious researchers, esp. if you are academic, or need to revisit certain keyword searchers regularly. https://harzing.com/resources/publish-or-perish
PDFDrive - another book download alternative to Scribd.com (and GenLib) https://www.pdfdrive.com/search?q=
Zotero - if you do writing and academic research, this is a must for reference and endnote management. OR if you have insane amounts of references, pdfs and keywords, like some of us. https://www.zotero.org/
Project Gutenberg - old, historically important, out-of-print and copyright free books scanned and searchable. https://www.gutenberg.org/
Worldcat.org