Whether or not RWBY actually qualifies as an anime is a matter of contention. Some people define anime by its style, while others define it by its country of origin. The problem with the first definition is that anime actually encompasses a wide variety of styles, making it difficult if not impossible to define it by any specific artistic elements. RWBY wasn't created in Japan - instead, it's an American production by the late Monty Oum and Roosterteeth. Though the team made many artistic choices that are common to anime, it's more accurate to call it "anime-inspired" than "anime."
This isn't to disparage it in any way - the fact that Western creators are using what's great about anime to enhance their own work is an example of a long history of cultural sharing between Japanese and American media. While RWBY isn't an anime per se, it has a lot in common with many anime series which make for excellent RWBY recommendations, like Soul Eater and Puella Magi Madoka Magica, as well as other Western shows that are influenced by the medium, like Avatar: The Last Air Bender, and Voltron: Legendary Defender. There are plenty more examples of anime similar to RWBY where that came from.
If you're a RWBY fan looking for something new to watch, check out one of these great anime like RWBY.
If you like RWBY, you probably like anime-inspired shows from Western animators that focus on a group of kids with incredible powers and wildly different personalities who have to work together to save the world from evil forces. If so, you'll probably like Avatar. Aang has been frozen in a block of ice for 100 years and is thawed out just in time to realize his destiny as the Avatar, the only person who can master all four forms of elemental bending. He and his friends must use these abilities to defeat the Fire Nation, which is waging war on the rest of the world.
If your favorite part of RWBY was the training that the protagonists received at Beacon Academy, you might also enjoy Soul Eater. Just as the characters from RWBY are learning to be Hunters and Huntresses who are powerful enough to take on Grimms, the characters from Soul Eater attend Death Weapon Meister Academy in the hopes of either wielding or becoming Death Scythes and take on dangerous threats to the world around them.
Sometimes you want to watch something with an anime-inspired art style but are in the mood for a more Westernized approach. If you're into RWBY, that might be a mood that strikes often. If so, Voltron: Legendary Defender might be a good next choice.
In a universe where an energy called quintessence fuels vehicles and magical abilities, the Paladins of Voltron must work together to pilot the large, interconnected mecha in order to defend the universe from the evil Galra Empire.
Puella Magi Madoka Magica is one of the most popular anime of the 2010s, so if you're an anime fan, you've probably seen it or at least heard of it before. But if you're a RWBY fan who missed out on Madoka, you should definitely add it to your watch-list. Like RWBY, it focuses on a group of girls who risk their lives to defeat beings that threaten the fate of their world. Also, while both of these shows have their moments of adorable humor, they can get seriously dark.