I remember when the phone first came out people were split into two camps, the first being conventional knowledge that closing apps saves battery, and the other being that leaving them open in the background actually saves battery because the phone doesn't need to load it fresh when you go back to it. Has there been a consensus?

This is a pretty controversial topic in the Android community and I just wanted to clear things up: do NOT clear apps from your recents menu.

Android apps are given as much of your phone's RAM as they need for them to function smoothly. However, when other apps on your phone need some of that RAM for them to function properly, Android takes away memory used from that app and lets any other app that needs that RAM use it. Apps that appear in your recents menu are essentially locked in memory: they are easily accessible, hence have much faster opening times and faster responses to any tasks initially. However, when you clear that app from your recents, the app is killed. This does more harm than good as it takes more resources to open the app after it's killed, straining your processor. This is why having more RAM is better as your phone can keep more processes running to ensure a smooth and lag-free experience.

Apps in your recents do NOT run in the background and drain battery, they take up very minimal resources and do not drain battery at all. They are activated when needed and put back to sleep when needed, Android has come a very long way in terms of how it manages background processes and has gotten pretty smart now. Well written and optimised apps do not always run in the background, they are only activated when needed.

Trying to kill an app to try save RAM and battery power will start an endless battle between the user and Android. The user will kill an app, Android will wonder "Hey, where did that go?" and put it back there. This whole process will drain battery instead of saving it so it's best to let Android do it's thing.

The only time you should clear an app from your recents menu is if it stops responding/is frozen or if it's an app you know you won't be using in a very long time.

That being said, now would be a good time to delete that RAM and battery booster app that you downloaded from the Play Store. These apps do essentially exactly all the unhealthy things I said above and always run in the background 24/7. Delete them, I seriously wonder how Google still allows these apps, don't be fooled by the 'positive' ratings that these apps get.

Lastly, free RAM is wasted RAM. The more free RAM you have, the slower your experience will be, not the other way around. Put that RAM to use, Android will thank you for it!

P.S. This one's for the advanced users out there: if you feel like your current kernel is bad at RAM management (less free RAM with minimal background apps) consider flashing a new kernel (through a custom recovery). Make sure you create a backup of your stock kernel first.

Edit: Taken from CNET:

In both Google's Android and Apple's iOS software, these apps are in a paused state in the device's memory that lets them open quickly. If you close each one, you'd be removing it from memory, forcing the app to reload from scratch the next time you open it. Depending on the app, this process may actually consume more battery life.