Just installed Sierra and wanted to see what works. So far from my testing the below work for me.
MOD EDIT: This is a wiki post, which is editable by anyone with the appropriate rights. Please update this post with compatible and incompatible apps to ensure the list is comprehensive. For apps with limited compatibility, please include a link to your post explaining the limitations. The lists are in alphabetical order.
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Compatible
1Password 6
2Do
Accordance Bible
Adapter
Adium (requires manual connection)
Adobe Acrobat Pro 10
Adobe Acrobat DC
Adobe Photoshop CC
Affinty Photo
Airmail 3
Alfred 3
Amphetamine
Aperture 3.6
Atom 1.7.4
BackBlaze 4.0.5.934
BetterTouchTool
BetterSnapTool
Blackmagic Disk Speed Test
Caffeine
CARROT Weather
Chrome 51.0.2704.84
Cloudmagic
coconutBattery
Coda
Continuity Activatin Tool
DaisyDisk
Dark Boot 4.0.6
Day One v2
Deliveries 2.0.1
Disk Inventory X
Downie 2.3.9
Drobo Dashboard
Dropbox
Duet (with iOS 10, although a bit choppy)
Evernote
Fetch 5.7.5
Final Cut Pro X (launches but have not used)
FileZilla
Firefox
Flux
Google Drive Desktop App
Handbrake (launches but have not used)
HardwareGrowler
Hardware Monitor
HoudahSpot 4.2.1
iDrive 3.4.0.15
iFlicks 2
iStat Menu 5.11
iStat Pro
Itsycal
Kodi
Letterspace v1.6.4
Little Snitch Nightly build 3.7 (
https://www.obdev.at/products/littlesnitch/download.html)
Magnet
Malwarebytes
Microsoft Office 2016
Mindnode
Minecraft 1.10
Mountain
MPlayer OSX Extended
MySQL Workbench 6.3.6
OmniFocus 2.5.3
OmniGraffle 6.0.4 (quite old)
OmniGraffle 5.4.4 (even older)
OpenEmu
Opera
Outside 1.1.2
ownCloud Client 2.2.0
PaintCode 2.4.2
Parallels 11.2.0
PDF Expert
Pinegrow Web Editor v2.9
Pixelmator (Magic Wand causes crash every time it is used, other than that no other observed issues)
Plex
Pocket 1.6.2
Polar FlowSync 2.6.4
PopClip
Quicken 2007
Quicken 2016
QuickSleep 1.0.1
Quiver 3.0.2
Reeder
Scrivener
ScummVM
Shazam
Sketch 3.8.3 by Bohemian Coding
Skitch 2.7.8
Skype 7.30(274)
Slack 2.0.3
Spotify (although slow to launch and ever the memory hog)
Steam
StuffIt Expander
SuperDuper
Text Expander 5.1.4
The Unarchiver
Transmission
Transmit
TunnelBlick
Tweetbot
Twitter
Vivaldi Web Browser (1.2.490.39) (64-bit)
VLC
VM Ware Fusion 8
Yummy FTP
XLD
Limited Compatibility
CleanMyMac 3 will prompt to install a beta release that supports Sierra (3.5b2)
Disk Sensei (launches but loses Trim support after restart)
Fusion 8.1.1 (see
this post)
gfxCardStatus (displays GPU status, but will always force discrete GPU since gfxCardStatus "requires" the discrete GPU)
Hazel (some rules do not work)
Simple Comic (will not install latest update but reads CBR files okay)
uTorrent (can crash in certain circumstances)
Logic Pro 9.1.8 (can crash intermittently)
Incompatible
Adobe Dreamweaver CS5 (crashes on launch)
Adobe Dreamweaver CS6 (must reinstall Java 6, opens and functions, crashes on Save As...)
Adobe Illustrator CS6 (installer error, if update from prior OS, make work after reinstall Java 6)
Adobe InDesign CC (installs, but has some rendering issues when dragging objects)
Adobe Photoshop CS5 (crashes on close)
Adobe Photoshop CS6 (installer error, make work if update from prior OS)
Bartender 2 (crashes at launch)
BusyCal (crashes at launch)
Carbon Copy Cloner 4.19 (installs and opens for use but does not actually backup)
Citrix Receiver
EazyDraw 7 (crashes at launch)
EtreCheck (crashes during scan)
Final Draft 9 (crashes at launch)
Fluid (any apps made with Fluid crash on startup)
Identify 551
iSkySoft iTube Studio 5.7 (crashes at launch)
Little Snitch 3.6.3 (see nightly build instead
https://www.obdev.at/products/littlesnitch/download.html)
Maintenance (crashes at launch)
Microsoft Office 2008 (crashes at launch)
Microsoft Office 2011 (Word, at least, crashes attempting to open a file)
Onyx (crashes at launch)
Pyware versions 8.0.0, 7, 6, and lower (due to Apple's MRJ Java--not able to be installed on 10.12)
RapidWeaver 7 (Opens projects and appears to work but crashes when previewing Site)
Safari Technology Preview 9.1.2
Scansnap Manager (crashes while trying to save the PDF)
Telegram (crashes at launch - someone recently claimed it worked. There's also Telegram Desktop to test)
Ulysses (crashes at launch)
Yosemite Disk Utility patched for El Capitan (crashes at launch)
Microsoft Onedrive (Crashes at Launch)
Western Digital Disk Tools (Complains about needing to be lauched from Applications folder)
Whatsapp Desktop (always recommends moving to Application folder when it is already there, and will lose login details prompting QR scans every time OS restarts)