Is rooting safe?

Solution
It's very hard to permanently brick your phone. There is pretty much always a way to fix it through adb/fastboot.

The real pros of rooting is almost complete freedom of your device, so you can do almost anything with it. Practical advantages are: adblocking, faster performance, sometimes better battery life, and lots of customization.

The downside is stability. Sometimes things can break if you run a custom rom or something. So make sure to make frequent backups in your custom recovery if you have one.
Rooting your phone is generally pretty safe. You need to research your particular phone. All the phones and tablets I've had it's very safe as there were factory flash files. So there was virtually no way to brick my devices. If something goes wrong, force the device into download, re-flash the ROM. For my devices this even worked for warranty purposes.

If you are rooting the factory rom there is very little risk. If you are installing a new rom, then a bit more. But again if factory files are available, there is virtually no risk on many devices.

Rooting will allow you to remove programs, and change things you couldn't otherwise change. Is it worth it to you? What do you want to do with root access? To the average user there is no benefit to rooting, and can be a security risk.
 
It's very hard to permanently brick your phone. There is pretty much always a way to fix it through adb/fastboot.

The real pros of rooting is almost complete freedom of your device, so you can do almost anything with it. Practical advantages are: adblocking, faster performance, sometimes better battery life, and lots of customization.

The downside is stability. Sometimes things can break if you run a custom rom or something. So make sure to make frequent backups in your custom recovery if you have one.
 
Solution
The chance to brick your phone due to root process is only below 2%. 98% is the possibility to succeed without any problem.
Root on Linux/Android == administrator right on Windows. It is worth to have root since you can do more and have more freedom with root access.
More freedom comes with risk, like mentioned above. The risk is if you are not familiar with your freedom, you could get some security risks.

Flashing custom ROMs is a different thing, to do this you need root access but you do not have to flash custom ROMs.
This is highly optional but people do this like as if this is part of root access.
Flashing custom ROMs then has higher risk of bricking your device but usually only software brick.
Software brick is almost totally harmless is you know your way to handle it.

The deadly part is the hardware brick, well...however the possibility of getting hardware brick is extremely small, I think it is below 1%.
I have never HW-bricked my phones since HTC-Hero until my current 1+1 and Z2, not even once.
I played around with various custom ROMs, compiled several myself, etc. but not a single HW brick.

Just be careful, according to my experience, ROM flashing can turn into addiction because it is quite fun to try custom ROMs. Your phone is like a whole new phone after each flashing, especially if you tried completely different ROMs.
 
It's safe but you've got to realize you are going to mess up at some point and have to "unbrick" your phone. With the right software, which is readily available in the rooted section, it is very simple to do. Sometimes it will be as simple as booting into recovery and restoring a backup. Other times you may need to use your computer and "flash" your phone with the stock software and then start over again which is still pretty easy....oh...and a little patience will help a lot.