I know a lot of people who are unhappy with PhotoBucket.
I am using Google Photos, which replaced Picasa. But it is more of a no-frills photo storage option, which is perfect for me.
For example it doesn't have the same share options that some of the others have, but that's OK it's easy enough (using FireFox or Chrome) to right click on the photo, click "Copy Image Location" and then paste the link into my post inside the "Image" tags.
Like this: [IMG]Image URL Goes Here [/IMG]
You can type the image tags or use the "Insert Image" button, select "From URL, uncheck "Retrieve file..." and paste the URL there. Either way works.
If you setup an account with Google Photo, you get a choice between "Original" and "High Quality" resolution.
If you select "High Quality" as your storage option, it automatically resizes your photos when you upload them (Down to around 800 pixels wide or so) but you get free unlimited storage/access to your photos. Not a big deal because the quality & resolution are plenty high enough for posting to forums.
If you "Original" resolution, then you get about 15 GB of free storage, then have to purchase more if you want it.
I use the "High Quality" option, and don't have any issues at all with the quality. I rarely post photos much bigger than 800 pixels wide anyway. Otherwise you have to start scrolling left & right to see the photo in a post.
If you have a Google Plus, or Gmail account you may already have a Google Photo account and just don't know it.