One of my favourite permaweb apps is actually one of the first, built by @Mazzz in early 2019. It is WeaveWatcher:
https://arweave.net/rvoldM5Y9LbQ46vLs29IAHfdv3ptqZb67g8xXRVeiDc
I use it as my browser 'new tab' page, so I can keep up with all of the exciting new stuff on the permaweb.
Thanks for pointing out WeaveNet, @b4a! I managed to miss that one.
-arweave-sam