Fighting games: Street Fighter IV Volt, Street Fighter X Tekken, King Of Fighters-i 2012, Soul Calibur.
If you only want one game from each genre, I'm sorry, but I can't help you. Chaos Rings 2 beats 1 and Omega, but I liked Drakerider more than Chaos Rings 2, but Chaos Rings 2 is longer and overall better than Drakerider. Omega's story was better than 2's. Then, about fighting games, my favorite game is SFxTK, but Volt, Soul Calibur and KOF-i 2012 have way more content. Soul Calibur is the only one which doesn't have online, but it's still really cool.
IDK about beat em ups and Bad Piggies.