I have my own preferred method of building strong passwords that has worked for me since I came up with it. The basis is coming up with a short sentence related to the account I'm creating--such as (and this is one I have never used) "I hate new passwords!"--and then crunching it together, capitalizing like a title, and inconsistently switching in some l33t-speak numbers--thus "IH4teN3wPa$sw0rd5!" Sadly, this does not help me remember passwords better (unless I use them frequently), but it does make them easier to type than the machine-made strong passwords.
Remembering the passwords requires writing them all down on a sheet of paper in the house (that I currently cannot find) or on documents to which I have online access, but are titled something innocuous like "New Story Ideas" with a portion of a false story filling the first page (again, I don't do this specific file name, but you get the idea). Unfortunately, not all of my passwords are on any one file. Today, I was looking for a password that I thought that I had remembered, but clearly did not, and discovered that it also wasn't written on any of the places that I had thought it would be. It was, however, accessible through the settings on my phone.
Having had one of my accounts hacked a year or two ago has made me more cautious with my passwords. Still, I can't help but be frustrated by the number and variety. I suppose that this is another First World, digital age problem.