We went with Photobucket back in 2006 with our first child. I also have a Flickr account that if I want a bunch of people to see it I’ll post it there, but I use that so rarely. PB has been great, and all I can say is decide on a filing format before you start uploading. ie: Pregnancy photos, family photos, just the kid photos. I just redid the file structure of ours and broke it down by child and year - yes I’m anal like that! Each child has a folder of the pregnancy, and then folders by year and within that months of that year (Child1 > 2006 > Dec06 … etc). I figure at some point both kids will be in the photos and that we’ll just have a general Family folder using the same year/month designation.
We try to be safe with the photos we post and we couldn’t see our families signing up to use services just to see our kids - even though we’d like that sense of security. I’ve tried to scale back on the # of photos I post, but the grandparents protest 
We have a 2nd child on the way in February and will continue to use PB.
I’m a Flickr Pro user, and I have been for quite some time. I like that it’s easy and it’s more about sharing than sites like Photobucket. I really wanted a site with a strong sense of community, but something that wouldn’t sacrifice on organization. I like the layout, tag system, sets, collections, etc. It just all works exactly how I want it to.
You do have to pay for it, but it’s worth it, and it gives people an easy Christmas present idea for me. 
Cool site, but I searched and searched and cannot find the pricing anywhere… how much does it cost?? Must be expensive if they hide the pricing information so well.
I like flickr the best, it seems to be the user friendliest and have the most features and options. It seems to be the one to use for people who want others to be able to look at all their photos. I mainly see people using photobucket if they are just posting a random picture to their blog or myspace page and need a place to host it.
Thanks so much for all the replies so far. I gave Photobucket a try but am finding it a bit fiddly. But that’s probably just me. I think I’ll try Flickr as well just to see if I get along with it better.
You’ve all been very helpful, thanks!
Oh and Lobsang your dog is lovely. Looks a bit like ours Frosty Fergus
If you hit the green ‘Try it!’ to the right, it’ll bring you to a listing of account types and prices.
I hate waiting for Flickr * p bucket, et al to load all the crap before they show the picture.
For sharing albums, Picasa seems to be fast loading for my dial-up friends and family. I still have the junk that goes with it but I can hot link to just a single clean pic if I want. I have other free sites that allow hot links to a single picture.
I use different sites for different things just as I will use any browser if that gets me better performance on a particular site.
I wish I could afford a static IP because using my own server to handle my pictures makes it super easy for me and those who are looking.