I can't offer any suggestions for emo or screamo. The only band that I listen to who could be considered Emo (and this is by other people's definitions, not mine) is Fugazi. But, I don't even listen to them much anymore.
Punk rock is more of an attitude in my opinion, so I think recommending 'punk' bands is a very subjective task. There are folk bands who are more 'punk' in their attitude and ethics than the bands that pass for punk now. Heck, the Beatles were more 'punk' than most of the bands labeled as punk, and no one would generally consider them punk. But, if I'm forced to recommend a punk band, I'd say either the Stooges or the Clash.
Hardcore? I'm at a loss here as well. I don't even know what it means. I know of some bands considered hardcore by some of my peers, but I don't listen to these bands.
Metal? There's lots of great stuff happening in metal right now. Its going for experimental and incorporating the sounds of other genres. Jesu would be my pick. Check out Jesu's Silver EP. Very groundbreaking metal. Pelican and Isis are two solid picks as well.
Indie is another nebulous term that I think is meaningless these days, especially since every one is such a hipster about the music they listen to. I'm 24 and when I first discovered real alternative forms of music (in about 1996), bands like Pixies, Sonic Youth, and Pavement were considered indie because of their independent status, attitude, and original sound. Things have changed, 'cause now you have MTV bands getting marketed as indie. Nonetheless, I think the best independent bands right now are Air, Flaming Lips, Sufjan Stevens, Boards of Canada, Animal Collective and M83. Those are just a few off of the top of my head. Obviously, there are many more. But, for me, Air is the most interesting of the bunch, and the most talented.
Experimental? Boards of Canada, Animal Collective and Air are all pretty experimental in their approaches to music.
Alternative? Pretty much any of the bands I've listed.