Towelroot is the best freeware to one click root any Android device. You can download Towelroot apk v3 on your device itself and root without using a desktop PC. Towelroot supports almost all Android devices including most popular devices like Verizon Galaxy S5, AT&T GS5, Nexus 5, GS4, Note 3.
Towelroot latest version has fixed many bugs for improve the Android rooting stability. The developer has mentioned that Towelroot most probably won't void KNOX warranty but there's a little possibility. So beware.
Towelroot is developed by Geohot. You can visit XDA forum for his original thread for release Towelroot. All crreditd are goes to the developer.