Most of us have registered our details on multiple websites such as Facebook, eBay and Strava, and most of us will use only one or two passwords for all of them. This wouldn't normally cause a problem, but if one of those websites has its password records stolen (as eBay did in early 2014) then the thieves can gain access to all of the sites where you've used the same login details.
We have two broad choices to fix this. Either we use (and remember) a different login credential for each website, or we use a tool that manages all of the credentials for us. Clearly there's a logistical issue with keeping track of multiple passwords, especially if we need to login to a website when away from home, and don't have the password list to hand.
Let's be clever for a minute and think about how to store all of our logins securely but with online access. A spreadsheet on Google Drive could do the job, right? Well, until recently you couldn't lock Google Drive access on your mobile device: once you'd authorised the app after installing it, you never enter a password again.
Now, however, Google Drive has a passcode feature! Tap on your account cog, scroll down to 'Passcode lock', turn it to 'on' and follow the instructions. You can now create a spreadsheet with your passwords in it.
NOTE that I don't advocate this as a very secure solution. It's just a way to keep different passwords for different websites, but you are of course listing all of your passwords in one document on a third-party service. Google (and whoever they authorise) can see the contents if they are so inclined. If this bothers you, then consider one of the specialist services below.
There are many providers of automatic cross-device password management. You can research them all if you like, but I have heard good things about 1Password and LastPass. A 2014 security review by the IET also reported positively on DashLane, Keeper and KeePass. The latter solution is the only free (and open source) one. When it comes to online security, however, it may be worth spending a little each year for the convenience and peace of mind.