With the latest firmware (2.60) the [tag]PSP[/tag] can read [tag]RSS[/tag] feeds, but it’s limited to audio feeds (aka [tag]Podcasts[/tag]).
According to this Digit LIVE article, [tag]Sony[/tag] says that the next firmware may include a RSS text feed reader if users request it. This would be a great functionality for the PSP, but there’s no information in the article on how you can request this new feature.