One of the last steps to launching your podcast will be to submit it to podcast directories like iTunes and Stitcher. Before you get started, make sure you RSS Feed is properly validated. If it's not, you could run into some trouble with getting your podcast accepted into some aggregators.
Top Podcast Directories
These are the directories that you need to get your podcast listed on. Most podcast listeners use these platforms to find, manage and listen to their podcasts.
Stitcher - http://stitcher.com/contentProviders.php
Google Play - https://play.google.com/music/podcasts/publish
Player.fm - https://player.fm/suggest
Spreaker - https://www.spreaker.com/broadcast
Podcast Submission Sites
If you search for websites to list your podcast on, you're probably going to be finding a lot of dead links. These directories have been around for a long time and will definitely help your podcast find new listeners.
AllPodcasts - http://www.allpodcasts.com/PingAll/Default.aspx
iPodder - http://www.ipodder.org/hints/new
Pod Directory - http://poddirectory.com/submit
PodKicker - http://www.podkicker.com/submitpodcast.php
Podcast Pup - http://www.podcastex.com/addpodcastform.asp
Plazoo - http://www.plazoo.com/en/addrss.asp
Podcast Blaster - http://www.podcastblaster.com/directory/add-podcast/
Several websites and apps pull data from sources like iTunes and Stitcher and will display your feed to new listeners on their platforms. Here are some of the apps that will automatically add your new show to their site.
I'll be updating this post regularly when I find new directories or aggregators, be sure to check this post again in the future for more.