Sure. If the format is MP3, then you can copy them to your Media Card and play them through the Media Player on the device.
Whether or not you can download them via your BlackBerry will depend largely on how the particular sites present the files on their sites. If they use Flash, then you won't be able to access that via your BlackBerry. Not all sites are compatible with mobile platforms.
I use an app called PodTrapper. Most amazing app on the BB. You enter the feeds, and it does the rest. Just like you'd expect. It can even hide the podcasts from BBMP so you can keep your music and podcasts from both showing up.
I use an app called PodTrapper. Most amazing app on the BB. You enter the feeds, and it does the rest. Just like you'd expect. It can even hide the podcasts from BBMP so you can keep your music and podcasts from both showing up.