In my childhood i have played some Browser Games (Oh those memorable games i played at ClickJogos), I Have played a lot of them, but i will tell a really good example:

KOF Wing 1.91 (& Other KOF Wing flash games):
Anyone has been aware of the KOF Series?, I'm aware of it (Everyone in Brazil are aware of this fighting game franchise & if you lived on a time that there was a lot of arcade centers & bars with decent game titles which made people spend coin to coin, there's a time where you had to count the moneys to see if you want to eat or play, then you had to buy 1 coin to play the fighting games in the arcades. The most popular fighting game is KOF 2002, Which was my favorite kof game from my childhood, played this a lot with my aunt Madalena which Leona Heidern was her favorite character. KOF 2002 Is a popular game here in brazil where i live at rio de janeiro, One of the most disappointing moments that traumatized brazilian players at most is a final boss named "Omega Rugal", which is a coin killer that made brazilian players spend lots of coins thanks to the genocide cutter & snk boss syndrome, Most players tried to avenge him.). And thanks to the internet that there's a memorable flash KOF Fangame named "KOF Wing, or The King of Fighters Wing" by chinese amateur group "FlashWing". It's a really decent flash game (I Like 1.91 version more because it's really smooth and adds the infamous coin killer/most hated boss by brazilians "rugal/omega rugal") with Non-KOF Characters such as Ryu & Chun-Li (From Street Fighter series), Moriya Minakata (From The Last Blade series) & Haohmaru (From Samurai Shodown series). The game shares effects from KOF2002UM (A KOF 2002 Remake that adds NESTS Saga bosses+characters that didn't appeared in the original game), CVS2, Eternal Fighter ZERO, Melty Blood Re-Act & etc. I Played alot this game as a little and like the officlal kof titles it was like button mashing, but i now know their attack commands.

KOF Wing 1.91 is a good suggestion for browser fighting games (The game is also avaliable to download with nests kyo secret character), There are some browser games that may be bad.