Jailbreaking an iPhone and Rooting a linux based system like Android are two completely different processes.
First question we'll tackle is "what is root?":
To have root access on a linux based system such as android means you have the equivalent access of Administrator on a Windows based computer. You will have unrestricted full access to nearly all aspects of the android system stack.
Second question "why would i want to obtain root access on my phone":
For those of us who would like an extreme level of control over our phone's files, root access is a necessity. Having a rooted phone gives the end user unprecedented control over the phone, enabling them to have limitless possibilities. Essentially unlocking your phone's full potential. With root/superuser access on your phone you would be able to flash modified roms (roms from other devices) , have access to certain functions on "root only" applications (example: wireless tether for root users - ability to tether your phone). The possibilities are endless.
Third question "how do i obtain root access on my phone (and keep it)":
To obtain root access, akin to jailbreaking, developers/hackers will need to find a system exploit that enables them root access. HTC devices such as the Tmobile G1 (HTC DREAM) and Tmobile Mytouch3g (HTC sapphire/magic) have been successfully rooted. Finding root is a matter of time, if it can be built, it can be broken. This translates to having the superuser.apk in the rom with the superuser binaries installed. Once you have root access you can continue to flash a customized recovery image (hold x + power on) and a compatible bootloader/spl (secondary program loader) which will in turn, enable you to flash custom modified roms (example: cyanogenmod)
In addition to voiding your warranty,
There are many risks associated with rooting your phone. The most apparent risk is bricking your device. If this happens,
Your phone is and forever will be, nothing more than, a brick.
So far, there are no software solutions for a bricked device. Your phone will be stuck at the splash loading screen indefinitely.
The only for sure way to brick your device is to corrupt both the recovery image and the secondary program loader and the actual rom itself (assuming you have a recovery image that can flash modified roms, an SPL that can fastboot, and a rom with root access)
As long as you have at least one of the three items listed, you are not the proud owner of a bricked device and can recovery your phone.
It is only when you are unable to enter recovery, fastboot, or your rom, and your device is stuck on the splash screen indefinitely, do you have a bricked device.
Also note that rooting your phone will block over the air updates that your carrier may provide you. You are pretty much consenting to opt out of OTA's; you have to update your own phone from now on.
How do I brick my device?:
In most cases, you really have to try, to brick your device. As long as one of the three safety’s built into your phone are functioning, you should have no problem resurrecting your phone. HOWEVER, the most common cause of bricking to date involves the flashing of the Haykuro “death/danger/special” SPL. A hacked developer SPL designed by Haykuro for the HTC DREAM, the SPL partitions the phone’s internal memory (therefore allowing end users to flash larger sized roms). Errors can occur when flashing the SPL or if the user flashes the SPL before flashing the complimenting system radio.
I hope this description was helpful enough for the majority of Droid users looking to root their devices. If you would like to expand your knowledge.