Going to recommend deviantArt. dA keeps the quality, is free, has no limits that I know of.

FurAffinity is good depending on how high the, er, rating of your work is. They thrive as a NSFW community in many cases so do bear that in mind, BUT they make up for it with harsh theft rules. They've had some issues with accounts being lost (I lost mine to the bug) in the last few years, but overall, a fantastic choice.

On the other hand...

Imgur has had issues with image loss in recent years, by the site pruning old files out. Not ideal long-term at this point. Overall, still one of the safest bets, but not exactly ideal.

Tinypic got in trouble with some games a few years ago for replacing images with NSFW content since they have absolutely no content filters. Just bear that in mind when using it. Also, they have more ads than a web page made in 2005. I personally don't recommend using them because I had content affected by this issue some years back and lost a few accounts on PG-rated sites.

Photobucket (we all know what site you meant, I'm assuming) is really trashy now and honestly isn't the place it was a decade ago. Such a shame.... used to use it all the time, now I don't bother to use it at all.