[Galaxy S III Themes and Apps] Kangburra:
I have a custom ROM running very happily with basic functionality, here is the list of apps kept and removed

AccuweatherDaemon.apk keep
AccuweatherDaemon.odex keep
AccuweatherWidget.apk keep
AccuweatherWidget.odex keep
AccuweatherWidget_Main.apk keep
AccuweatherWidget_Main.odex keep
AllShareCastWidget.apk
AllShareCastWidget.odex
AllSharePlay.apk
AllshareMediaServer.apk
AllshareMediaServer.odex
AllshareService.apk
AllshareService.odex
AnalogClockSimple.apk
AnalogClockSimple.odex
AnalogClockUnique.apk
AnalogClockUnique.odex
ApplicationsProvider.apk keep
ApplicationsProvider.odex keep
BCService.apk keep
BCService.odex keep
BackupRestoreConfirmation.apk keep
BackupRestoreConfirmation.odex keep
BadgeProvider.apk keep
BadgeProvider.odex keep
BestGroupPose.apk
BluetoothAvrcp.apk keep
BluetoothAvrcp.odex keep
BluetoothMap.apk keep
BluetoothMap.odex keep
BluetoothTest.apk keep
BluetoothTest.odex keep
CSC.apk keep
CSC.odex keep
CapabilityManagerService.apk keep
CertInstaller.apk keep
CertInstaller.odex keep
ChatON_MARKET.apk
ChocoEUKor.apk
ChromeBookmarksSyncAdapter.apk
ChromeWithBrowser.apk
ClipboardSaveService.apk keep
ClipboardSaveService.odex keep
ClockPackage.apk keep
ClockPackage.odex keep
ContextProvider.apk keep
ContextProvider.odex keep
DSMForwarding.apk
DSMForwarding.odex
DSMLawmo.apk
DSMLawmo.odex
DeepSea.apk
DeepSea.odex
DefaultContainerService.apk keep
DefaultContainerService.odex keep
DialerWidget.apk
DialerWidget.odex
DigitalClock.apk
DigitalClock.odex
DigitalClock21.apk
DigitalClock21.odex
DirectConnect.apk
DirectConnect.odex
DirectShareManager.apk
DirectShareManager.odex
Divx.apk
Divx.odex
DrmProvider.apk keep
DrmProvider.odex keep
Dropbox.apk
DropboxOOBE.apk
DttSupport.apk keep
DualClockAnalog.apk
DualClockAnalog.odex
DualClockDigital.apk
DualClockDigital.odex
DualClockDigital42.apk
DualClockDigital42.odex
EdmSysScopeService.apk
EdmSysScopeService.odex
EdmVpnServices.apk
EdmVpnServices.odex
EnterprisePermissions.apk
FFFFFFFF000000000000000000000001.drbin keep
FWUpgrade.apk
FWUpgrade.odex
FaceLock.apk keep
FactoryTest.apk
FlashBarService.apk
FlashBarService.odex
FmRadio.apk
FmRadio.odex
FmmDM.apk
FmmDM.odex
FmmDS.apk
FmmDS.odex
FotaClient.apk
FotaClient.odex
GMS_Maps.apk
GameHub_2.0_ICS.apk
Gmail.apk
GmsCore.apk keep
GoogleBackupTransport.apk keep
GoogleCalendarSyncAdapter.apk keep
GoogleContactsSyncAdapter.apk keep
GoogleFeedback.apk keep
GoogleLoginService.apk keep
GooglePartnerSetup.apk keep
GoogleSearchWidget.apk keep
GoogleSearchWidget.odex keep
GoogleServicesFramework.apk keep
GoogleTTS.apk
GroupCast.apk
Hearingdro.apk
HelpHub.apk
HelpHub.odex
HelvNeueLT.apk
INDI_Server.apk keep
InputDevices.apk keep
InputDevices.odex keep
JobManager.apk keep
JobManager.odex keep
KeyChain.apk keep
KeyChain.odex keep
Keystring_DFT.apk keep
Keystring_factory.apk keep
Keystring_misc.apk keep
Kies.apk
Kies.odex
Lcdtest.apk
LogsProvider.apk keep
LogsProvider.odex keep
LuminousDots.apk
LuminousDots.odex
Magnifier.apk
Magnifier.odex
MediaUploader.apk
MobilePrint.apk
MobilePrint.odex
MobileTrackerEngineTwo.apk
MobileTrackerEngineTwo.odex
MoreServices.apk
MoreServices.odex
MtpApplication.apk keep
MtpApplication.odex keep
MusicFX.apk
MusicFX.odex
MusicHub_30.apk
MusicPlayer.apk
MusicPlayer.odex
NetworkLocation.apk keep
Nfc.apk
Nfc.odex
NfcTest.apk
NfcTest.odex
NoiseField.apk keep
NoiseField.odex keep
OmaCP.apk keep
OmaCP.odex keep
OmaDrmPopup.apk keep
OmaDrmPopup.odex keep
PCWClientS.apk keep
PRUI.apk keep
PRUI.odex keep
PackageInstaller.apk keep
PackageInstaller.odex keep
PanningTryActually.apk keep
PanningTryActually.odex keep
PaperArtist.apk
PartnerBookmarksProvider.apk
PartnerBookmarksProvider.odex
Personalization.apk keep
Personalization.odex keep
PhaseBeam.apk
PhaseBeam.odex
PhoneErrService.apk keep
PhoneErrService.odex keep
Phonesky.apk keep
PhotoWall.apk
PhotoWall.odex
PickUpTutorial.apk keep
PickUpTutorial.odex keep
PlusOne.apk
PolarisViewer.apk
PopupuiReceiver.apk keep
PopupuiReceiver.odex keep
Preconfig.apk keep
Preconfig.odex keep
PreloadInstaller.apk keep
PreloadInstaller.odex keep
RCSe.apk
RCSe.odex
RoseEUKor.apk
SMemo.apk
SMemo.odex
SMemoProvider.apk
SMemoProvider.odex
SNS.apk
SPPPushClient_Prod.apk
SPlannerAppWidget.apk
SPlannerAppWidget.odex
SSuggest.apk
SamsungApps.apk
SamsungAppsUNA3.apk
SamsungCamera.apk keep
SamsungCamera.odex keep
SamsungIME.apk keep
SamsungIME.odex keep
SamsungTTS.apk
SamsungWidget_FavoriteApp.apk
SamsungWidget_FavoriteApp.odex
Samsungservice.apk
SecBluetooth.apk keep
SecBluetooth.odex keep
SecBrowser.apk
SecBrowser.odex
SecCalculator2.apk keep
SecCalculator2.odex keep
SecCalendar.apk
SecCalendar.odex
SecCalendarProvider.apk keep
SecCalendarProvider.odex keep
SecContacts.apk keep
SecContacts.odex keep
SecContactsProvider.apk keep
SecContactsProvider.odex keep
SecDownloadProvider.apk keep
SecDownloadProvider.odex keep
SecDownloadProviderUi.apk keep
SecDownloadProviderUi.odex keep
SecEmail.apk keep
SecEmail.odex keep
SecExchange.apk
SecExchange.odex
SecFactoryPhoneTest.apk
SecFileShareClient.apk
SecFileShareClient.odex
SecFileShareServer.apk
SecFileShareServer.odex
SecGallery2_Galaxy.apk keep
SecGallery2_Galaxy.odex keep
SecHTMLViewer.apk keep
SecHTMLViewer.odex keep
SecLauncher2.apk keep
SecLauncher2.odex keep
SecLiveWallpapersPicker.apk keep
SecLiveWallpapersPicker.odex keep
SecMediaProvider.apk keep
SecMediaProvider.odex keep
SecMms.apk keep
SecMms.odex keep
SecNoteMyFiles.apk
SecNoteMyFiles.odex
SecOmaDownloadProvider.apk keep
SecOmaDownloadProvider.odex keep
SecPhone.apk keep
SecPhone.odex keep
SecSettings.apk keep
SecSettings.odex keep
SecSettingsProvider.apk keep
SecSettingsProvider.odex keep
SecSetupWizard.apk keep
SecSetupWizard.odex keep
SecTelephonyProvider.apk keep
SecTelephonyProvider.odex keep
SecWallpaperChooser.apk keep
SecWallpaperChooser.odex keep
SecurityProvider.apk keep
SecurityProvider.odex keep
SelfTestMode.apk keep
SetDefaultBrowser.apk
SetDefaultBrowser.odex
SetupWizard.apk keep
ShareShotService.apk
ShareShotService.odex
SharedStorageBackup.apk
SharedStorageBackup.odex
SimServicePermission.apk keep
SimpleAlarmClock.apk
SimpleAlarmClock.odex
SimpleFavoritesWidget.apk
SimpleFavoritesWidget.odex
SlideShow.apk keep
SlideShow.odex keep
SmartcardService.apk
SmartcardService.odex
Stk.apk
Stk.odex
Street.apk
SyncmlDM.apk
SyncmlDM.odex
SyncmlDS.apk
SyncmlDS.odex
SysScope.apk
SystemUI.apk keep
SystemUI.odex keep
TMServerApp.apk keep
TMServerApp.odex keep
Tag.apk
Tag.odex
Talk.apk
TopicWall.apk
TopicWall.odex
TrimApp_phone.apk keep
TwDVFSApp.apk keep
TwDVFSApp.odex keep
UserDictionaryProvider.apk keep
UserDictionaryProvider.odex keep
Velvet.apk keep
VideoHub.apk
VideoPlayer.apk
VideoPlayer.odex
VoiceRecorder.apk
VoiceRecorder.odex
VoiceSearchStub.apk
VpnDialogs.apk
VpnDialogs.odex
WAPPushManager.apk
WAPPushManager.odex
WeatherWall.apk
WeatherWall.odex
WebManual.apk
WebManual.odex
WfdBroker.apk
WfdBroker.odex
WlanTest.apk
WlanTest.odex
YahoonewsDaemon.apk
YahoonewsDaemon.odex
YahoonewsWidget.apk
YahoonewsWidget.odex
YahoostockDaemon.apk
YahoostockDaemon.odex
YahoostockWidget.apk
YahoostockWidget.odex
YouTube.apk
kieswifi.apk
kieswifi.odex
mcRegistry keep
minimode-res.apk keep
sCloudBackupApp.apk
sCloudBackupProvider.apk
sCloudDataRelay.apk
sCloudDataSync.apk
sCloudSyncBrowser.apk
sCloudSyncCalendar.apk
sCloudSyncContacts.apk
sCloudSyncSMemo.apk
serviceModeApp.apk
talkback.apk
voicetalk.apk
wssyncmlnps.apk keep
wssyncmlnps.odex keep