I personally prefer Google reader from the browser for reading RSS feeds. I can star, share and mark as read just as easily as some of the apps I tried.

I've grown to really like Listen for podcasts. It's fairly simple but works well for my needs.

I'm sure there are other options out there but those are what I'm using now!

 

BeyondPod and Doggcatcher are the two best in my opinion. I use BeyondPod.

 

For the RSS Reader, I LOVE NewsRob. It syncs beautifully with Google Reader.

 

BeyondPod will do both! I use it just for podcasts and I highly recommend.

 

+1 for DoggCatcher. It's takes some configuration to get it working (at least the way I wanted it to), but now it's my "it just works" app. Since I try to pad my morning commute with podcasts, having it just work is key. It also handles RSS subscriptions, but I don't use it for that so I couldn't comment on how well it does it. I've never been a big RSS fan anyway. Worth the money (not a free app).

 

newsrob and acast for me

 

BeyoundPod has been great. I don't buy many Apps but this one is worth it. Plus you can try it free for a week to see what you think. It does both RSS feeds and Podcasts very well.

 

Doggcatcher for podcasts, NEWSROOM for rss, you will not believe how FANTASTIC it is until you try it