You updated to iOS 8 and found that the Podcasts app from Apple is already installed! It's great if you use the Podcasts app actively (like some users) but if that app is of no use to you, it's just sitting there, eating up some space. You want to delete/remove the Podcasts app but you can't. What do you do now?
There's one tiny workaround involving restrictions. It's easy. And while it can't get rid of the Podcasts app forever, it will ‘hide' it from everywhere on your iPhone or iPad (homescreen, app lists, Spotlight etc). It's not technically “removing” or “deleting” the Podcasts app, but it sure is a way to stop it from appearing on your iPhone/iPad.
How to Hide/Remove Podcasts App from your iPhone/iPad in iOS 8:
Step #1. Open Settings
Step #2. Tap on General
Step #3. Tap on Restrictions
Step #4. If you've set Restrictions already, enter your “Restriction” passcode (not the phone's lockscreen passcode) alternatively If you've not set Restrictions already, tap on Enable Restrictions. Enter a restriction passcode (twice) to set it up.
Step #5. Now, switch off the toggle for Podcasts.
This will “hide” the Podcasts app from your homescreen (and in fact, from everywhere). You won't be able to access it from anywhere.
Just like Podcasts, there are other apps like iBooks which you can remove (read: hide) if you don’t want them.
Note that removing/hiding the Podcasts (or other apps) through this process does not remove the app or its data. They're still at large, on your iPhone/iPad. And it's easy to show Podcasts back on the homescreen again: just toggle the switch in Restrictions labeled Podcasts to ON.
Arguably, you're entitled to say “what the heck is this?” because like I said before, it's not really a solution. But as the saying goes, some solution is better than no solution. As long as Apple thinks that this should be a part of the default package, all future upgrades to iOS will install the Podcasts (and iBooks) app too.