[Xperia Z3 Q&A, Help & Troubleshooting] android404:
What I uninstalled using titanium backup without facing issues:

Anonymous Data 1.0 (com.sonymobile.anondata)
Anonymous Usage Stats 1.0 (com.sonyericsson.idd.agent)
ANT HAL Service 4.0.0 (com.dsi.ant.server)
AR effect 3.3.23 (com.sonymobile.androidapp.cameraaddon.areffect)
AR fun 2.1.11 (com.sonymobile.androidapp.cameraaddon.arfun)
Backup & restore 1.0.A.1.6 (com.sonymobile.synchub)
Backup over MTP 1.2 (com.sonyericsson.mtp.extension.backuprestore)
Backup-Restore 1.0 (com.sonyericsson.backuprestore)
Black Hole 1.0 (com.android.galaxy4)
Bubbles 1.0 (com.android.noisefield)
Chrome 39.0.2171.93 (com.android.chrome)
com.sony.snei.np.android.account (com.sony.snei.np.android.account)
com.sonyericsson.android.omacp (com.sonyericsson.android.omacp)
com.sonyericsson.mtp.extension.update (com.sonyericsson.mtp.extension.update)
com.sonyericsson.music.googlelyricsplugin (com.sonyericsson.music.googlelyricsplugin)
com.sonymobile.backgrounddefocus (com.sonymobile.backgrounddefocus)
Configuration Agent 1.0.1 (com.sonymobile.deviceconfigtool)
Creative effect 1.0 (com.sonyericsson.android.addoncamera.artfilter)
Docs 1.3.492.11.35 (com.google.android.apps.docs.editors.docs)
Download music info 3.3.A.0.7 (com.sonyericsson.metadatacleanup)
Drive 2.1.495.05.35 (com.google.android.apps.docs)
DUALSHOCK™ series 1.0 (com.sonymobile.dualshockmanager)
DUALSHOCK™3 wireless controller 1.0 (com.sony.nfx.service.WirelessControllerManagerService)
Email 8.0 (com.android.email)
Enchanted forest 1.6.A.0.15 (com.sonyericsson.androidapp.everchwallpaper)
Enterprise Service 1.0 (com.sonymobile.enterprise.service)
Exchange Services 6.1 (com.android.exchange)
Face in
picture 1.0 (com.sonymobile.android.addoncamera.dual)
File Commander 3.1.13142 (com.mobisystems.fileman)
Google App 4.1.24.1672412.arm (com.google.android.googlequicksearchbox)
Google Play Games 2.2.05 (1620489-008) (com.google.android.play.games)
Google Play Movies & TV 3.6.14 (com.google.android.videos)
Google Play Music 5.7.1788Q.1634597 (com.google.android.music)
Google Play Newsstand 3.3.1 (com.google.android.apps.magazines)
Google Text-to-speech engine 3.4.6.1819666.arm (com.google.android.tts)
Google+ 4.8.0.81189390 (com.google.android.apps.plus)
Info-eye™ 1.8.08 (com.sonymobile.androidapp.cameraaddon.infoeye)
InitialBootSetup 1.0 (com.sonyericsson.initialbootsetup)
Keep 3.0.03 (com.google.android.keep)
Lifelog 2.4.P.1.4 (com.sonymobile.lifelog)
Movie Creator 2.3.A.0.7 (com.sonymobile.moviecreator.rmm)
my*Xperia 0.0.A.0.77 (com.sonymobile.mx.android)
News & Weather 2.2 (1623380) (com.google.android.apps.genie.geniewidget)
Photo Analyzer Service 5.7.A.0.3 (com.sonymobile.photoanalyzer)
Photo editor 23.1.A.0.2 (com.sonymobile.china.photoeditor)
Portrait retouch 23.1.A.0.2 (com.sonymobile.android.addoncamera.selfportrait)
Simple Home 1.2.1.A.0.7 (com.sonymobile.simplehome)
Sketch 6.0.A.1.1 (com.sonymobile.sketch)
Social live 1.0.24 (com.bambuser.sociallive)
SocialEngine 5.0.A.0.1 (com.sonyericsson.socialengine)
Software update 3.0.0.A.0.13 (com.sonyericsson.updatecenter)
Support 1.1.29 (com.sonymobile.helpapp7)
Timeshift burst 1.2.0.0 (com.sonymobile.android.addoncamera.timeshift)
Video Unlimited 14.0.A.0.7 (com.sony.snei.vu)
What's New 2.0.A.0.11 (com.sonymobile.entrance)
Wikipedia extension 5.0.A.0.8 (com.sonyericsson.music.wikipediaplugin)
Xperia Calendar Sync 5.0.A.0.1 (com.sonyericsson.androidapp.fbcalendarsync)
Xperia Social Engine Photos 5.0.A.0.1 (com.sonyericsson.socialengine.plugins.facebook)
Xperia Social Engine Photos 5.0.A.0.1 (com.sonyericsson.socialengine.plugins.picasa)
Xperia™ Chinese keyboard 23.2.A.0.1 (com.sonyericsson.textinput.chinese)
Xperia™ Japanese keyboard 3.0.A.0.6 (com.sonymobile.pobox)
Xperia™ Lounge 2.9.10 (com.sonyericsson.xhs)
Xperia™ Lounge Pass 1.0.1 (com.sonymobile.xperialounge.services)
Xperia™ Web Runtime 1.3.0.1.17 (com.sonymobile.webview)
Xperia™ with Facebook 7.0.A.0.3 (com.sonyericsson.facebook.proxylogin)
Xperia™ with Twitter 2.0.A.0.1 (com.sonymobile.twitter.account)
YouTube extension 5.0.A.0.8 (com.sonyericsson.music.youtubeplugin)
YouTube karaoke extension 5.0.A.0.8 (com.sonyericsson.music.youtubekaraokeplugin)

Some of my apps that require root:

Adaway - blocks ads

Greenify - puts apps to sleep when they're not needed.

Better battery stats - helps identifying energy hungry apps.

Afwall+ - Firewall

Recently - makes the recent panel useful again.

I use Tasker with the secure settings plug in (root) to manage brightness, sound, lockscreen security,... And then you have the seemingly endless world of xposed modules, e. g. Xprivacy, true silent mode, app settings, unicon, notify clean, 20mp superior auto, Xperia xposed,...

If you want to, you can stop using your phone and just mod it all day long ;)