I know there was a discussion previously BUT they didn't talk about security. E.g.: if I root my phone will all my apps run with root permission?
Related: Are there any risks to rooting a device?
The answer is no: not all application will have root permission. Not all the apps require root and the apps requiring root will not have it unless you give them permission to do so. At least that's what I can tell after using z4root and superoneclick to root a few phones. You get a superuser app that will get requests from apps needing the root account and you'll have the option to enable that or not. Risks connected to rooting a device are, more or less, the risks connected to using an administrative user on any kind of Unix-like system.
Ever tried a
rm -R (a command to delete all files) on GNU/Linux?
It's like putting in the recycle bin your Windows folder and empty it just because you're a root user and you can do it.
Superpowers always involve super responsibilities and super attentions :)
Said that I have to say that in my everyday use (with a little brain turned on) I can't see a real way to get any kind of harm. But if you install strange scripts coming from al quaeda and tons of pirated apps and poor not certified code... Well. Bad things could happen.
Install a recovery and do a nandroid backup. After that play happily with your phone :)
If you root your phone, then only the applications that you explicitly grant root access to will have root access. This does make things fairly safe, as that extra step should be enough to make you stop and think "Why does this app need root?".
If you only grant root access to apps that need root for a good reason, are from trusted developers, and which you acquired from a trusted source then you should be ok.
Bear in mind what apps with root access can do though - from a previous answer on the subject:
On a rooted phone, an app which has been granted root access can do pretty much anything that is possible in the hardware. Apps that have root permissions can write on non-read-only storage media (including modifying the bootloader), modify other programs' private data, modify system settings, modify system files, etc. A rooted app can also hide itself from the system, and pretend to be uninstalled while being perfectly well and alive.
I'll let you imagine what the worst-case scenario security implications are for a nefarious app being granted root access on your phone; be careful out there.
The newest versions of SuperUser (3.x) support using a PIN to approve root access for apps. In other words, whenever an app requests root you need to enter your PIN before root access is granted. This is more or less foolproof; no app should be able to get root access on its own or through you clicking the wrong button without it exploiting some bug in SuperUser or the system, and if it's doing that you might be screwed even without root.