I've been using
www.diverecord.com for years.
It's easy, you can put as much or as little information into the logbook as you like, and you can even upload pictures of your dives. I've checked out at least a half dozen or so other online logbooks and in my opinion they don't even come close.
Another cool feature is that it calculates your "Recreational Dive Index" based on the dive details you provide, such as depth, visibility, conditions, etc...and you can compare your experience with that of the dive community in general.
You can also upload your certifications (and at one time) including scans of the front and back.
HOWEVER
I don't believe the site is being actively maintained because I have repeatedly emailed scans of new C-card certifications and I have received no response.
My guess is that no one is minding the shop however the site has been up for many years, it's used quite extensively and I'd like to at least think it's not going anywhere.
I suggest printing out the dives every so often, it's a site feature. I have about 170 dives logged on that site and I figure even if the site goes down I could reproduce the logbook elsewhere in about 2 hours.