The best IMAP client for Gmail in Linux

Thunderbird should be good, if you are intending to use a separate email client

Gmail is a tad special. Either you want to use insert your favorite IMAP client here or you don't. The assumption for using gmail is that you'll be using the web interface. If you want fast offline access for it with all the gmail features, I'm pretty sure that's why they invented gears and maintain an offline gmail project.

Update: Okay so lets run down the requirements:

• multithreaded and responsive even on large folders [Check, relies on Firefox for this]
  2. integrated with Gmail spam filtering (report spam) and archive features [Check, it basically is Gmail]
  3. capable to deal with Gmail folder names (which depend on language settings in Gmail!) [Check, ditto]
  4. using some standard local storage (maildir, mh, whatever) [Sorry, not with this, but does it matter if you get all the other points?]
• with quick local search (or integrated with any desktop search engine) [Use Google Desktop or the regular Gmail search in offline mode.]
• good and convenient in offline mode [Check, It really works, you even get a desktop icon]
• aware of various i18n issues [Check, only in so far that Gmail does]

Bonus, There's a spotty connection mode that gives you like-live usage with buffering for inconsistent internet responsiveness.

Apart of Thunderbird i found Claws-mail, which was quite convenient in the matter of memory consumption for my old laptop. It's available under yum in Fedora repositories (should be in apt-get in Debians as well).

Thunderbird is probably the easiest way to achieve this, just make sure you set it up to fully download all emails/attachments, not just the message headers (from here):

An IMAP account normally only downloads headers to the hard disk when checking for new mail. Your account would have an "Inbox.msf" file but no "Inbox" file. When you read a message it is fetched from the server unless its already cached in memory. If you want to maintain a local synched copy of a remote folder use "Tools -> Account Settings -> Offline & Disk space -> Offline -> Select folders for offline use". That will store/update a copy of the selected remote folder as an mbox file, which you can only see when working offline.

..but, since you mention mutt, perhaps Fetchmail?

Fetchmail retrieves mail from remote mail servers and forwards it via SMTP, so it can then be read by normal mail user agents such as mutt, elm(1) or BSD Mail. It allows all your system MTA's filtering, forwarding, and aliasing facilities to work just as they would on normal mail.