Replay Music splits tracks when detecting silence (if this mode is not disabled). So stream buffering can be a problem when using it.

High quality video and audio streams normally require high speed connections (Cable, DSL). But in many cases you can record high speed media streams even if you have a slow connection (Dial-Up).

Note that live (continuous) streams could not be recorded at a speed higher than your connection speed. To record on-demand (seekable) streams on a slow connection with a higher speed you should change the bandwidth settings (only for streams having multiple bit-rates). Depending on a stream recorder it should be done in a recorder itself or in a player like Windows Media Player, Real Player.

I use 33.6 dial-up connection and here are some examples of recorded streams:
1. I've successfully recorded several Indian songs recently using Replay Music (Real Media on-demand video streams).
2. I've successfully recorded video lectures of the US university using RM Recorder (Real Media on-demand video streams).
3. I've successfully recorded high quality music videos from AOL music using Replay A/V (Nullsoft video on-demand video streams).
4. I've successfully recorded Windows Media videos from a video blog using WM Recorder (Windows Media on-demand video streams).
5. I've successfully recorded videos from YouTube using Replay A/V (Flash .FLV on-demand video streams).
6. I've successfully recorded music from web radio stations using StreamRipper Winamp plug-in (Shoutcast/Icecast MP3 live audio streams).

Bottom line:
1. You can record any on-demand stream on a slow connection
2. You can record slow live streams on a slow connection
3. Direct sound recording software like Replay Music can be used on a slow connection, if you find streams that will not be buffering when playing (you can increase buffer size used by your internet media player).

All stream recorders/rippers are free or free to try, so you don't really have to buy them before testing on your favorite streams.

And I suggest you to use free Replay Media Guide to find interesting audio/video streams and podcasts.