I use Botophucket... sorry, photo-bucket. Have done for probably ten years of more.
Was a free way to increase my alloted free web-space for my hobby-site, when my ISP gave 50Mb and thought that 'generouse'
Free account gave me a wopping 1 Giga-bite to host photo's!
They have made numerouse 'upgrades' over the years, to the up-loader sortware... this tends to be the main area of messing, and it's always a contension.
Anoyingly, most free hosting sites don't support any 'direct' access to server space. In the ood days that was FTP access... you had to buy the pro-services for such stuff, so you were left with the 'House-Wife-Freindly' web-portal, that often only let you upload one image at a time, and would often regect anything over accepted file size, or auto-re-size.
They have got better over the years, though and P-B has had a 'bulk' uploader for a while, and latest version launched this year is a neat 'drag and drop' affair.
But they have changed the interface, and accessing albums can be a bit slow, while they have half hiden the pre-tagged image links.
There's then some limited photo-ed functions.
I basically use it JUST to host images pre-edited for display; so just a matter of getting them up-loaded and organised in albums, and that sussed, its easy enough to use.
One 'nice' thing about Photo-Bucket is that they retain your original file-name.
I've not used Flikr... and from what I have seen of it.... it's trying to do a lot more by way of allowing viewer as well as uploader comments like You-Tube, and 'stuff'... rather than just hosting, and gets rather more convoluted about image protection.
I use Face-Book. Mostly for family snaps. Its where the kids look, isn't it? Meand I can restrict access to some degree with family or freinds lists, but I can still right-click to gain image URL to display the picture on a web-page or forum if I manually stick the tags I need round it. Face-book doesn't retain original file-name though, so you cant do it 'blind' and construct the img url, without getting it off FB.
Couple of 'subscription' hosting sites linked to dedicated camera software have presented themselves to me; one Kodak-Easy-Share, came with a compact, and tried offering me a Kodak hosting site 'free trial'.... likewise Nikons ViewNX... I have tried neither.... they may, for a price, make it easier to go straight from camera to web... but that benefit is marginal, I think.
Basically... if they are free..... sign up for a web-mail address... so you can give them an e-mail account on sign up.... sight up... and try them out.... see which you preffer, and does best what you want.