There's multiple replacements for Adobe Flash Player, the most popular one being the implementation of HTML5 on the web.https://en.wikipedia.org/wiki/HTML5
As for why it's so vulnerable, pretty much because Flash Player (like Adobe Reader, Java, Silverlight, etc.) is one of the most installed program in the world. Which means that if hackers finds an exploit (0-day) in it, they are sure to target a large number of users. They want to hit the biggest portion of users if possible and Flash is a way to achieve that goal. Right now, there's a lot of discussion about Adobe Flash Player being insecure because three 0-day exploits were found in the leak from Hacking Team (they got hacked and 400GB of confidential data got leaked). Now they are all patched in Adobe Flash Player 220.127.116.11 but it's still a good wake up call that tells people around the world that the time they relied on Flash is coming to an end and for a more secure web, it needs to be dumped and replaced completely.