As a general rule, any software which interferes with the in-game player experience between when you press “Play” and the end of game screen is against the rules.
Although these programs are allowed, many are classified as “use at your own risk”. Riot’s stance may change, so it’s important you stay informed if you choose to use these programs.
Also, ensure all your programs features are allowed under the rules. If it has one feature that breaks the rules, then using the program is illegal, even if you only use the legal features.
These are allowed for now, on the condition that they aren’t providing a competitive advantage. Remember the program must only do custom skins, if it breaks the rules in other ways it will be bannable (like MKLoL).
Completely allowed if there are no additional features. Currently Curse Voice (version 6.1.X), Razer Comms (version 2.1.X) and Discord are confirmed to be allowed.
These programs are allowed because they use legal features supported by the Riot API. LoLReplay and SkinSpotlights Tool are officially confirmed to be fine.
These programs are allowed because their function is no different to visiting OP.GG or LoLNexus. LoLWiz (Overwolf mod), LSI and Championify are a few of these programs which have been confirmed to be allowed.[634,635,636]
Allowed, but on a strong “use at your own risk” basis. The majority of VO applications don’t seem to provide any competitive advantages.
These programs are against the rules. Using them puts you at a serious risk of being permanently banned.
“The following are examples of behavior that warrant disciplinary measures:
ix. Using any unauthorized third party programs, including mods, hacks, cheats, scripts, bots, trainers and automation programs that interact with the Software in any way, for any purpose, including any unauthorized third party programs that intercept, emulate, or redirect any communication between the Software and Riot Games and any unauthorized third party programs that collect information about the Game by reading areas of memory used by the Software to store information.” 
Changing your screen resolution through the game.cfg to an unsupported resolution is not allowed. Using programs to change your resolution, frame of view, or “zoom” is also bannable.
Any scripts, like macros, which automate actions on your behalf are bannable. Even in-game chat macros are not allowed.
497 https://ask.fm/RiotLyte/answers/131116484802 ; Page 199