I used to use Kodakgallery, but now they have a minimum purchase requirement based on how many pictures you have. I had over 3,000 pictures up there so I had to purchase at least $20 worth of photos or they said my pictures would be deleted. I was rather upset, so I bought pictures and switched to a new website for future pictures.
So, now I switched to Shutterfly and absolutely love it. My favorite feature is the share site. It's great for making a website for your baby pictures. And it's still free unlimited photos.
Actually, if you sign up for Shutterfly and make a share site, you'll get like 20 or 30 free prints. Right now I have free offers for a 20 page 7x9 photo book and 50 free prints. It's really easy to get free prints. You should sign up just to get the free prints at least. :)
The software Shutterfly Studio is pretty good too. You can easily organize your photos and sort through them by keyword, dates, or folders. And it does all the features you're asking for...crop, red eye, etc.