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In addition to those suggestions, you can simply turn mobile data off when you don't want to use it (I suggest this because in your post you don't mention anything that obviously needs a constant data connection amongst your essentials).
Every phone has different apps so it's hard to give a list. On many phones you can disable preinstalled apps so they wont run or use data, but you must root to uninstall preinstalled apps:
1. Go to your phones Settings menu.
2. Tap Apps (or Applications).
3. Go to the All tab, you might need to swipe right/left to get to it.
4. Scroll down to the app you want to disable and tap it.
5. If Force Stop can be chosen tap it first, then tap Disable.
Be careful as disabling some system apps could cause your phone to not function correctly.
To save on data:
Some apps use background data, which means they use data when you're not using the app. You can disable background data on an app by app basis so they wont use your mobile data when you're not using them. Some phones might not have this option though.
1. Go to your phones Settings menu.
2. Tap Data Usage
3. Scroll down to the app and tap it.
4. Scroll down and tap to check Restrict Background Data.
For some apps you wont get some updates/notifications after after doing this when you're not using that app. Also I believe that only shows apps that have already used data so with a brand new phone there might not be many apps listed yet.
Or you can disable all background data > Settings > Data Usage > Menu > Restrict Background Data. If Restrict Background Data is turned on here you wont have the option to disable it for each app as described above. There is also an option to turn off Auto Sync Data.

If an app is disabled it shouldn't be running, you shouldn't even be able to see it's icon.I have Verizon Moto G. I just noticed with my apps disabled, including my call blocker which in a must have, they appear to be running under the "running" category.
Don't disable Google Play, or the com.android com.qualcomm system stuff, but you can usually safely disable apps likeThere are so many to list, like Google Play services, Google Play games, Google Keyboard, Translate, com.qualcomm, etc.
The problems with this request is:There are so many to list, like Google Play services, Google Play games, Google Keyboard, Translate, com.qualcomm, etc.
So rather than list all the apps, can you tell me which ones would be safe to disable/remove?

The problems with this request is:
a) there are a lot of apps which are safe to disable/remove, so what you are asking is for us to write a long list rather than you doing it
and
b) the list of apps installed depends on the device, software version & carrier, so we don't know all of the apps that come pre-installed on your device.
So I don't think there's any way we can give a comprehensive list. At best a few suggestions as @kate has done.
Can you not find a call blocker which doesn't require a continuous data connection? I'm not sure why that would be needed for the functionality, unless it relies on online list of spam numbers. (I have very few blocked numbers, and just use my phone app's blacklist for this, so have never used a dedicated call blocker app).
If an app is disabled it shouldn't be running, you shouldn't even be able to see it's icon.
Don't disable Google Play, or the com.android com.qualcomm system stuff, but you can usually safely disable apps like
Google Books
Google Games
Google Movies
Google Music
Google Newsstand
Live Wallpapers
Some Verizon apps might be safe to disable, others might be needed.


My point was that there is a very long list of stuff you can disable or removeHadron (A) I already stated "there are too many to list"! No I am Not asking "so what you are asking is for us to write a long list rather than you doing it" But to the contrary, "which ones would be safe to disable/remove?"
