Is there a way to log into and root my device without using ADB? With the Android SDK it is possible to run the "adb shell" command to shell into an Android device plugged in via USB. I would like to know:


Is there another way to log into an Android device and gain root access
to all its files and folders without having to install the Android SDK,
for instance using Putty somehow once the device is connected via Wi-Fi
to a router on a common network?
On Unix there is a program called "last" allowing you to see the most
recent logins and the associated times. Is there a similar utility
that can be run on Android once root access is gained that would
allow you to view the most recent times when the device was used
or unlocked?
There are several ways to achieve root access on an Android device -- and they differ a lot, depending on manufacturer, device, Android version, and even Linux kernel version running. Unfortunately, devices don't ship with "root" accounts (as we are used to from our desktops and laptops) -- but there's no common way to "root" them.

Rooting is mostly done via Exploits. Some require ADB installed and an USB-Session established. Others do not require ADB. And again others ship as a single .apk to be copied to the device and started there (so-called "one click root"). And again another method might involve a custom recovery being flashed...

So many methods. But to explain them all in detail, this is not the right place -- while your question should be answered already, as it required only a "yes" or "no" :)