For downloading from one-click hosting sites, there is JDownloader (powerful, java-based, will cost you some memory - see installing page) and Free Rapid Downloader (cross-platform, portable).
Internet Download Manager works bad in Wine, and a perfect replacement -- there is none. But do we need it? ...
If you thought you knew the maximum download speed of your connection with Win/IDM, try AXEL and really boost your speed - and even make it your default download manager in Firefox and Chrome. For tricky links that are not accepting default download try to paste link in terminal using Axel or Prozilla.
IDM could download delicacies like Arte +7: a special program does just that, with a very easy to use interface.
To handle torrents - a specific post here.