FFXIVPADS http://xivpads.com/
Useful for tracking your progress with quests, ethers, achievements and so on. Much better overview than on Lodestone. The developers actually invite people to contribute to the project. Basically it is a PHP parser that reads data from Lodestone and presents it in a much better way then Lodestone itself.

TheKrizz http://tehkrizz.net/FFXIV/downloads.php
Here you can get all the updates and patches as direct downloads. Very useful if you do not like to use the slow update download process which is integrated in the game itself, do not like to use alternative torrents or need to setup the game on a new machine. There is a guide on how to do it (last steps in installation guide). You do not need to download ALL of them if you start from zero. There are some that include previous ones. Best you start FFXIV and note down which patch version it tries to download. Install that one and repeat this process until the game is up to date. It goes much faster then using the game's own update downloader (which seems to be a torrent-client or soemthing similar in the background).

Mooglebox http://www.mooglebox.com
For looking up recipes, food effects and stuff. Seems to be more up to date then its alternativs currently. One nice thing is also their mob camp location tool and their gathering location tool.

Yellow Gremlin http://ffxiv.yg.com
Used to be a good place for looking up recipes and so on. But seems a bit out of date now. It is still useful to find out names of leves and items etc. in another game language, when auto-translate does not help. Also helpful for finding locations of drops, NMs, NPCs and comments of users on those. However, a bit out of date.

ZAM http://ffxiv.zam.com
Same as Yellow Gremlin, but only in English.

FFXIV-DB http://www.ffxiv-db.com
Another database on items and recipies. Thanks to Demon for the hint.

FFXIV Maps http://ffxivmaps.com/
Well, the title says it all

FFXIVPro http://www.ffxivpro.com/
For statistic nerds. Lags quite a bit behind in updating the stats though.

Disciples of the Land http://www.disciplesoftheland.com/
Guides and information for DoL

Lodestone http://lodestone.finalfantasyxiv.com
Well, other than concerning patch and event information etc., I do not find it too useful. Maybe the forums can be interesting.

FFXIVCore http://www.ffxivcore.com/
English player forum. Info on updates, patches etc.

FFXIVOrigin http://www.ffxivorigin.com/
English player forum. Info on updates, patches etc. Seems to be quite dead, currently.

German player forum http://www.final-fantasy-14.de/
Only interesting for Germans of course.

FFXIV Log Parser http://ffxiv.curseforge.com/addons
One of many parsers that are around. It will parse the logs for battle information. You might wanna use it to optimize your group tactics or just to show-off how much dps you make.
I do not use any parser, but many linkshells use it for end-game boss fights.

ElitePVPers http://www.elitepvpers.com/forum/final-fantasy-xiv/
Not specialized on FFXIV. But you can find information on modding, programming parsers and bots as well. While I do not like using bots, it is still interesting for modders and programmers. You will also find information on how to customize your UI configuration, model viewers, changing game music and so on (generally modding) in the forums. Be careful with links posted in the forums. Some might contain harmful stuff or explicit adds and stuff like that. So be careful when follwing any links. Moreover, be aware that some tools and guides that users post there might not be in line with Square Enix terms (bots, exploits, hacks, modification of game data are definitely not in line with the terms). Using them might even result in a server ban. So be aware of what you are doing. Still it is interesting for some of us and I think, other then some more dubious sites which I would not link to here, I can link to this forum.

Sandboxie http://www.sandboxie.com/
One of many dual-box solutions. You can easily google for more solutions and guides in different languages. I do not actually dual- or multibox. So I cannot provide mor information on it. As far as I know, dual-boxing is not expressively forbidden in Square Enix terms. And I do not see why it should be.

Server Status on ZAM http://ffxiv.yg.com/server-status
If you wonder why you cannot login sometimes, this is one of the places to go in oder to check Server status.

Enjin Signature Generator http://www.enjin.com/tools/ffxiv-signatures
Enjin also provides services for hosting LS pages. Just like Guildwork.

FFXIVsign http://ffxivsign.free-h.net/
Another signature generator

FFXOrigin Signature Generator http://www.ffxivorigin.com/tools/signature/
One more signature generator. But I think it uses Enjin in the backgound. This page also shows server status.

Market price databases
There have been some attempts to establish databases for market prices. However, I do not find any project that seems to be up to date. Maybe one of you knows one? One approach on ZAM is http://ffxiv.yg.com/bazaar.

thanks for the usefulness of this information

FFXIVOrigin has been dead for a long time ever since the in-game linkshell fell apart. It hasn't had a upgrade since that time. I'm the only one who has more than 5posts who posts there. Other posters are usually people asking for buddy passes, ask a question and never come back after, or people looking for members for their linkshell. There might be some useful guides for main storyline quests but I would say most the other information is out dated.

Another database site I use is ffxiv-db.com. I like it better for items since you can filter by dated and new gear.

I added Demons comments and some page where you can get direct downloads of patches. Saved me a lot of time. Extremely useful if you reinstall the game or install it on another machine. As all patches are signed by SE (which is checked on installation), you can trust that those are the original unmodified files.