How has nobody mentioned Log Horizon? It's an amazing anime based on people trapped in a world similar to a video game. Sort of like Sword Art Online, except it actually has character development, world building, relatable characters, and a lack of huge gaping logic flaws. Other action anime that I can think of off the top of my head are Code Geass and Baccano. Watch those too.
If you're looking for some feels, you can watch Clannad, although you may have to get used to the art style. Or if you're feeling lighthearted, watch the Comedy-Slice of life series Nichijou.