ar.vyrd

Automated or otherwise comprehensive

4archive: all boards; users request for individual threads to be auto-archived
4chanarchive.net: formerly 4chandata.org; /3/, /a/, /adv/, /an/, /asp/, /cgl/, /ck/, /co/, /diy/, /fa/, /g/, /gd/, /int/, /jp/, /k/, /lit/, /m/, /mlp/, /mu/, /n/, /o/, /out/, /p/, /po/, /sci/, /sp/, /tg/, /toy/, /trv/, /tv/, /vp/, /v/, /vg/, /vr/, /w/, /wsg/, /x/; shitty interface, used to carry images but removed all of them as of 20 November 2014, at which time it also stopped archiving anything
archive.moe, foolz.us's new home: /a/, /biz/, /c/, /co/, /diy/, /fit/, /gd/, /h/, /i/, /int/, /jp/, /k/, /m/, /mlp/, /out/, /po/, /q/, /qa/, /r9k/, /s4s/, /sci/, /tg/, /tv/, /u/, /v/, /vg/, /vp/, /vr/, /wsg/; used to carry /sp/ as well (stopped Dec. 2014); picked up /fit/ from imcute.yt (?) after the latter's death
cliché.net: /e/; alt: md401.homelinux.net/4chan; went down for a while starting in late 2013, but as of March 2015 is back, albeit with text only; /jp/ archive appears not to be set up
desustorage: /mlp/, /qa/
fgts: alt: fgts.eu; /asp/, /b/, /cm/, /h/, /hc/, /hm/, /n/, /p/, /qa/, /r/, /s/, /soc/, /y/
love is over: /c/, /d/, /e/, /i/, /lgbt/, /t/, /u/, /w/, /wg/; second incarnation, attempted to take over archiving /v/ in 2013 and went under for a while; kept nyafuu's archives while it was in limbo and will be dropping /c/, /e/, /w/, and /wg/ once the latter is fully set up again
not4plebs: /sp/
nyafuu: /c/, /e/, /w/, /wg/; stopped archiving late August 2014 but is back as of March 2015
4plebs: /adv/, /f/, /hr/, /o/, /pol/, /s4s/, /tg/, /trv/, /tv/, /x/
rbt: alt: rbt.asia; /cgl/, /con/, /g/, /mu/, /qa/, /w/; used to archive /soc/ (now under the auspices of fgts)
suptg: /tg/; threads manually added
swfchan: /f/lashes only
warosu: /3/, /biz/, /cgl/, /ck/, /diy/, /fa/, /g/, /ic/, /jp/, /lit/, /sci/, /tg/, /vr/

Dead

bui's archive: /b/; died in December 2013
chanarchive: formerly 4chanarchive.org; all boards, plus other chans; users voted for individual threads to be archived; very, very dead as of June 2014
deniable plausibility: /v/, /vg/ (being updated with the old foolz database)
foolz: alt: http://green-oval.net/cgi-board.pl/board/thread; /a/, /biz/, /c/, /co/, /diy/, /gd/, /int/, /jp/, /m/, /out/, /po/, /q/, /sci/, /sp/, /tg/, /tv/, /vg/, /vp/, /vr/, /wsg/ (used to carry /v/); migrated to archive.moe (August 2014)
nsfw foolz: /u/
foolz a shit: /adv/, /asp/, /cm/, /d/, /e/, /i/, /lgbt/, /n/, /o/, /p/, /pol/, /s/, /s4s/, /t/, /trv/, /y/
heinessen: alt: maidlab, xfiles; /an/, /fit/, /k/, /mlp/, /r9k/, /toy/, /x/; died late 2014, dumps of boards moved to imcute.yt and archive.moe (/k/)
maware: /t/
imcute.yt, heinessen mk ii; unfortunately, died very quickly in early March 2015: /an/, /fit/, /gif/, /int/, /mlp/, /out/, /qa/, /r9k/, /toy/
installgentoo.com: alt: archive.installgentoo.com; had /g/, /t/; gives 403 errors as of June 2014
installgentoo.net: died in March 2014; had /diy/, /g/, /sci/; database merged into warosu
no-ip: /3/, /adv/, /an/, /ck/, /co/, /fa/, /fit/, /int/, /k/, /mu/, /n/, /new/, /o/, /p/, /po/, /pol/, /r9k/, /soc/, /sp/, /toy/, /trv/, /v/, /vp/, /x/; died ca. early 2012
nth-chan: /vg/; died after a few weeks
sharethreadarchive: /mu/ sharethreads only
thedarkcave: merged into foolz (now of course archive.moe); had /c/, /int/, /out/, /po/
thisfile: /f/lashes only
world athletic project: /adv/, /b/, /cm/, /con/, /d/, /e/, /h/, /hc/, /pol/, /r/, /s/, /s4s/, /soc/, /trv/, /u/, /y/; died October 2013 because of rampant CP

Personal/selective thread collections: see rx. for links and information
As of now, there don't appear to be any boards without automated archives. Note that a much better listing is kept by the Archive Team, you should really just go there.

Updated 2015/03/21.