I'd strongly recommend Pocket Casts. One extremely nice feature is that if you have multiple devices (including iOS ones) it will remember where you're up to in each show across devices.
The other killer is that they manage the episode refresh check through their servers so it's a single operation for your device to check for new stuff, instead of it having to go out and check (in my case >50) individual sites like other apps.
The other killer is that they manage the episode refresh check through their servers so it's a single operation for your device to check for new stuff, instead of it having to go out and check (in my case >50) individual sites like other apps.