I would like to replace default Firefox's download manager with some free Firefox's add-on which:
- would allow me to "click" all links I need and then download "one file at time" and in order I select
- would (auto)resume broken downloads
- is stable

Any recommendations?

Personnally, I use Downthemall https://addons.mozilla.org/en-US/firefox/addon/downthemall/

It is stable, it is accepted by most sites out there and it allows autoresume downloading. I use it for example for big downloads on Oblivion's mods and it works perfectly. It's also not a ressources hog so it won't slow down your computer.

No other propositions? :)

Get FlashGot.
It can integrate many download managers, is stable and can download multiple stuff on a page at once.
Things like auto resume and one file at a time have to be supported by your selected download manager

I use DownThemAll as well, it works great and has plenty of options. I'm not too familiar with other download managers for Firefox, but I would recommend it for the same reasons that xa_chan posted.

One of the comments on FlashGot page is: "Love this addon, works terrific with DownThemAll." Does that mean these are two plugins for two different things?

Somewhen in the past I was trying to use FlashGot but didnt notice any "useful things" so uninstalled.

FlashGot is an plugin, which integrates external download managers into firefox, but isn't an download manager itself.
It's still neat, if you're want to download with system tools (like wget) or have an manager, which doesn't integrate well.

Technically, it's not a Firefox add-on, but JDownloader works pretty well for downloading multiple files simultaneously.

JDownloader is a dream come true for those who use online file-sharing sites (e.g. 4shared, Mediafire. Filesonic). I wish I'd heard of it a lot earlier than I did, it would have saved me so much time and grief.


-Khalaq

Since really long time I have no reason to use any file sharing site. The only one is probably Imageshack, but it is for images only. As far I can remember these mentioned cities are overloaded with ads and some waits are required (that was one of the reason I stopped using them). Anyway, how does JDownloader help in there?

well, you generally just have to add the url of the file to JDownloader and it handles everything (wait times, caps to enter, etc...) It is very handy, even if it is completely different from Downthemall, of course.

I also use DownThemAll, teamed up with DownloadHelper for embedded video sites such as Youtube.

oh yeah, download helper is good too!!

So for now, recommendations are:
- DownThemAll
- JDownloader
- FlashGot
- DownloadHelper

It also seems like first one has the most votes? Now the question is should I install all of them or 1-2 will be enough.

In the past, when I was using Windows 95 I remember some shareware downloader, called GetItRight (? or similar?). It had good option to download one file from a few different sources at the same time. Can I find such option today somewhere?

Check out Free Download Manager. It does everything GetRight did, plus it's free. :) I use FlashGot for Firefox to push downloads to it which also makes it easy to grab embedded videos and such.