I've always used the free TCPMP as it supports just about any stream format (excluding real). It has settings for what file formats are associated with it. As for Shoutcast I use the classic version at
http://classic.shoutcast.com as it seems to use less resources. Mobile browsers usually either open the file or offer the option of saving them. I keep the .pls files in a "stream" folder. I either download them on the phone directly or I get the .pls files on my pc and transfer them. Winamp is good for saving the AOL/CBS stream addresses.
I use the free Roku stream snooper to find the address of streams that want to use an embedded player. I either use Winamp to save them as .pls files or sometimes just manually use a text editor to create them.
On TCPMP I create a .pls file of several streams that I listen to. By using the next function, which TCPMP allows you to map to a hardware key, I can jump from one stream to the next by just pushing one button. Quite handy while driving.