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From my understanding, a rooted Android phone mean that the user will be accessing everything on the phone, just like a root user. So, installing a Apps mean that the Apps will also have root privileges.
So, does a non-rooted ones more safer than those rooted phone? (In another word, will rooted Android phone make it a easy target for Apps that are actually malware or virus to attack?)
With root privilege, a malware app can certainly do heavy damage, but it doesn't work like that.
Just because an app is on a rooted device, it doesn't mean it gets root privilege automatically. With modern rooting standards, you'll have to permit it. When an app requests root access, a pop-up from SuperUser or SuperSU app appears asking to allow it or not. If you don't know much about the app, simply block access. If you don't pay attention to this, you deserve to experience bad things.
Update:
As a last line of defense, I'd like to add that nobody knows from where nasty malware apps can exploit a loophole. You find un-rooted devices secure, but there're apps which are able to even root a device from inside (There was a positive-purpose app named Root Exploit in Google Market which was later kicked out by Google). So, if you want to be secure, don't install unknown apps. And, if possible, use Play Store only. These suggestions are irrespective of your device is rooted or not.
OTA RootKeeper. Anyway, I have added it to answer. Thanks...
Yes, and No.
If an app had root access, then it could cause untold damage - but you have to specifically give it that access.
The SuperSU or Superuser apps allow you to specify which apps have root access, and what commands they run. You can use this to stop malicious apps, and to also determine malicious apps.
So, to conclude:
