I noticed there is no sticky thread with links to all the important websites and patches for new users like for many other games, so I decided to make one. I haven't played all of the games, so please fill me in if I missed something.
Ultima Codex: Ultima fansite with many ressources (successor to Ultima Aiera)
The Codex of Ultima Wisdom: a Wiki covering the entire Ultima universe
Ultima Wiki - Editable Codex: Another Ultima Wiki
Strategy Wiki: a Wiki for game walkthroughs, has very good guides for the Ultima games and, more importantly, features comprehensive lists of key mappings, spells, items, maps and all sorts of useful stuff
Replacementdocs: hosts all sorts of video game documentation, in case something is missing among the GoG extras or if you want to see the manuals of other versions of the games
Ultima Retrospective by The Spoony One: funny and (more or less) informative video series looking back at the Ultima games. Keep in mind that Spoony is an entertainer, not a critic, so take everything with a grain of salt.
DOUG the EAGLE's Pages: Cheats, tools, and various ways to break the games and other fun stuff.
Pix' Ultima Patcher: (scroll to miscellaneous) a Patcher for most (all?) of the Ultima games to apply fan-made patches in one go instead of each one manually (Windows only?)
High-Resolution Ultima Map Project: High-Res scans of the original cloth maps, superior to the maps included with the GoG releases
Ultima Savegame Editor for Ultima 1 - 5 for Windows and Mac OS X (instructions for Boxer and the GoG versions included)
Ultima Font Collection: Various fonts used throughout the Ultima series
All games in the series, with the exception of Ultima IX, can be played in DOSBox. GoG sells the DOS versions already bundled with DOS Box, so Windows users don't have to do anythig special to get the games running.
Users of other OSes can get the games running in DOSBox as well, but they will need to get the game files somehow out of the installer. The easiest way would be to install the games and then take what you need and throw the rest away. Mac users should take a look at [url=http://boxerapp.com/]Boxer instead of DOSBox, it's basically the same thing, but Boxer is more user-friendly and imports the right DOSBox settings from the GoG installs. Instead of plain Wine, Mac users can use Wineskin, which is more user-friendly and can make standalone Wine ports (I use it myself to port many of my Windows games)
The DOS versions of these games are often inferior compared to other ports, usually having less colour, less detail and no music. There are various fan-made patches to upgrade the old games to other ports' standards.
A general note about the upgrade patches: Some (all?) of the patches were made to be used under Windows, so they won't run in DOS or DOSBox on other OSes. In that case there are additional files provided, which you must put in the game's directory, as you did with the patch. Do not put the folders containing the files inside the game's directory, you need the files themsevles, not their folders.
For example, I want to patch Ultima II, so I download the ZIP file. I extract it and get two folders (BIN and MANIFEST) with several files. I take the files from these folders and put them in my Ultima II directory and throw the two folders away.
The ZIP file is also attached as an image to this post just in case. Download the "image" file and change the extension from PNG to ZIP; I had to do this because the GOG forum software only lets me upload image files.
I have the Mac version, where are my files?
GoG is using a custom standalone version of Boxer to make the games run out of the box. To access the gamebox (wrapped up DOS files) right-click on the app, choose "Show Package Contents" and then navigate to Contents -> Resources and find the bile with the .boxer extension. You can access a gamebox's contents the same way.
You save files are in another location though. You can find them under "~/Library/Application Support/Boxer/Gamebox States/[name of your game]/Current.boxerstate/[name of your game].harddisk/". In the case of Ultima 1 this would be be "~/Library/Application Support/Boxer/Gamebox States/com.gog.ultima-1/Current.boxerstate/C Ultima1.harddisk/".
How do I delete my old characters in the Mac version?
You could use the aforementioned path and delete the files or just choose from the menu bar of the game File -> Reset Game Data
Charater Advancement: a general overview about leveling up in the Ultima series, since the process is never really straight-forward.
-- Age of Darkness --
Ultima I: The First Age of Darkness
To clarify one thing, there is no upgrade patch available for the DOS version of Ultima I, since the DOS version was released later than the other versions as a remake.
Computer Ports of Ultima I
[url=http://strategywiki.org/wiki/Ultima_I:_The_First_Age_of_Darkness]Ultima I on Strategy Wiki[/url]
Ultima II: Revenge of the Enchantress
Computer Ports of Ultima II
[url=http://strategywiki.org/wiki/Ultima_II:_The_Revenge_of_the_Enchantress]Ultima II on Strategy Wiki[/url]
Ultima II Upgrade Patch: If you are trying to patch the game on a Non-Windows OS you also need these files.
Ultima III: Exodus
Computer Ports of Ultima III
[url=http://strategywiki.org/wiki/Ultima_III:_Exodus]Ultima III on Strategy Wiki[/url]
Ultima III Upgrade Patch: If you are trying to patch the game on a Non-Windows OS you also need these files.
-- Age of Enlightenment --
Ultima IV: Quest of the Avatar
XU4 - Ultima IV Rebuilt (status: Beta, playable): a source port to run Ultima IV natively on modern systems
Computer Ports of Ultima IV
[url=http://strategywiki.org/wiki/Ultima_IV:_Quest_of_the_Avatar]Ultima IV on Strategy Wiki[/url]
Ultima IV Upgrade Patch: If you are trying to patch the game on a Non-Windows OS you also need these files.
Virtues in Ultima IV (overview how the game tracks your virtues and how to improve them best)
Ultima V: Warriors of Destiny
Computer Ports of Ultima V
Ultima V Upgrade Patch: If you are trying to patch the game on a Non-Windows OS you also need these files.
Runeless font: replaces all the rune characters in the game with normal latin characters.
FIXPARTY.EXE: this DOS exectuable fixes your Ultima IV save file (PARTY.SAV) if you get an error when trying to import a U4 character. Run the EXE, type the letter of the drive that has the save file and that should do it.
Ultima VI: The False Prophet
Nuvie (status: in development, play- and beatable): a source port to run Ultima VI natively on modern systems
Computer Ports of Ultima VI
[url=http://strategywiki.org/wiki/Ultima_VI:_The_False_Prophet]Ultima VI on Strategy Wiki[/url]
-- list continued here in another post due to length --