If you are online, you can not escape passwords. I began using KeePass for password storage on my pc several years ago. Initially, I had the KeePass Portable on a USB drive. That way, I could plug the USB drive into whatever computer I happened to be on and have access to my passwords. When Dropbox became available, I decided to use it as storage for my password database. This requires loading KeePass on each computer I use or I can still use the USB version. This way, I do not have to have the USB drive to access my passwords. I simply point my local copy of KeePass to the proper Dropbox file. This keeps the database synced across all computers. Here are the steps required to accomplish this.
1) Load KeepPass on each computer you will be using (Home PC, Work PC, Laptop, etc.)
2) Using KeePass, create a DB and store in a Dropbox folder
3) Load Dropbox on each computer in step 1
4) Open Keepass on each computer and access the password db in Dropbox
Access on Android devices
When Android phones and tablets came out, I needed the same passwords on these devices. Fortunately, KeePass and Dropbox are available as Android apps. Follow theses steps to set up KeePass on Android devices.
1) Download and install the Android versions of KeePass and Dropbox.
2) When opening KeePass, point to the Dropbox password database which was created in step 2 above.
The KeePass db is encrypted and password protected so I don't worry that it is stored in the cloud. This approach has worked very well for me. You could also use Google Drive, SugarSync, or other online storage sites in the same way.