I like some of the older Hardcore. Stuff like Black Flag, Agnostic Front, Botch etc. I haven't listened to much of the newer stuff, but I do like Hatebreed and, my personal favourite, SSS (although they could probably fit under the thrash umbrella, but I consider them a hardcore band. Awesome live too).

Also, I must admit, I am a fan of the new 'Hardcore'/scene bands, such as Bring Me The Horizon.