For a long time now I have been using imgur, but I got to thinking and wondered if there was a better site.
It would be nice if the site also allowed linking directly to the image file instead of having to go to their site. Also, an option to delete the image in-case I accidently dox myself after posting a screenshot.
After a bit of searching, I found PasteBoard and ImageVenue, but I haven't tried them out yet.
Most are trackerware. I was using Post Images but they ban your IP if you bypass their tracker links and link to images directly. If you only have a few images, or you don't mind kicking a guy a few bucks for self hosting there is catbox.moe. If you're only needing temporary hosting that same guy has litterbox.moe.
If you are concerned about posting images directly to the larger instances, don't be. They have cheap third party storage options setup, and all the images are cached on the instances anyways. External hosting is only helpful for long term storage and small instances that host communities. It wouldn't hurt to kick a buck or two into the pot to help the instances you use a lot. It's like $5 per terabyte per month for 3rd party storage.