If you're having sudden high data usage, here are some things to check.

Step 1: Uploads or Downloads?  How much vs normal usage?

First a good thing, if you can tell from your ISPs traffic page (or by asking), is to determine if most of the traffic is being uploaded or downloaded. 

Under most normal Internet usage, your downloads will be much higher than your uploads (by a factor of 10 or more), so it's worth noting the ratio.

Also take note of when the usage jumped up, and what your average usage was like before it suddenly increased.

Step 2: Narrow down the device responsible

Try turning off one device at a time (eg. a Computer, a Laptop, an iPhone) for a day, and check if Internet usage drops accordingly.  If so, you've found your likely culprit, so start there.  If not, try turning them all off for a day, see what happens (leave your router on).

It's important to note that with some devices, screen off doesn't mean device off. Make sure you completely power down the device - on portable devices, usually this involves unlocking the device and holding down the power button until a menu or slider appears to power off the device.

Step 3: What has changed?

Have your habits changed?  Have you started using a streaming service such as Netflix, Hulu Plus?  Have you installed new software?  All of these can have an impact on usage.  Think about what has changed recently and you may find the culprit.

Have you increased your connection speed?  A lot of services, especially video streaming and p2p services, use adaptive bitrates - so the faster your connection, the more data will be used.

It's a Device on my network!

If turning off one of your devices stopped the excessive data, have a closer look at the device, here are some likely suspects.

Uploads are high:

* Torrent software - for example uTorrent, Transmission

Torrents can produce a lot of traffic, as while you download an item, you also upload it (sometimes several times over).  Go into the software and confirm that you're not seeding something ad infinitum.  Or exit/remove the software completely.

* Spotify

Unbeknownst to many, the Spotify client includes a P2P component which streams your library to other users.  This can generate a lot of traffic.  If uninstalling isn't an option, these instructions may help you to disable it, or you can become a premium subscriber and run in offline mode.

* Apple iCloud / Dropbox / Mega / Skydrive / Google Drive

Some applications sync a lot of data to, and from, the "cloud" - these can be a candidate for high data usage and may be working quietly in the background without your knowledge.  Check settings on your devices to see if they are syncing a lot of photos, videos, or files to the cloud and decide if this is something you want.

* Windows 10

Windows 10, by default, allows P2P sharing of Windows updates to other Windows 10 PCs on the Internet, which Microsoft calls "Windows update Delivery Optimization".  

More information is available at the below link, including instructions to disable:

http://windows.microsoft.com/en-nz/windows-10/windows-update-delivery-optimization-faq

Downloads are high but Uploads seem normal:

* Software updates

Many devices and applications automatically download updates, for example, Macs, iOS devices, Android handsets, Windows Update, Steam to name a few. Check on each one and disable automatic updates, see if this helps with usage.  It's possible that an update is failing to download, and keeps being retried.  Check the status of any updates in progress.

It continues even if all my devices are switched off!

But nothing's switched on except for the router, what could be using my bandwidth?  Well, typically you are billed for anything that comes across your connection.  Keep in mind your Internet router is also a computer, so it can be responsible.  Here are the most likely suspects in this case:

* Firewall / UDP Amplification

The firewall setting on your router - is it turned off for any reason?  Turn it back on, preferably set it to the default setting, and see if data usage drops.

Sometimes with it switched off, the router will listen on its public IP address for certain types of requests, and can be used as part of certain types of attack known as UDP Amplification attacks.  These are increasingly common, and can generate a great deal of traffic on your connection - even if you have no other devices switched on. 
 
* Unauthorized Access via WiFi

Could someone have guessed your wifi password or obtained it by other means?  Make sure you're using WPA security, and set a strong password.
If your router has a feature called "WPS" then switch this off as well.

* Another modem with your user details

Did you sell a modem that might have had your configuration details on it?  With some ISPs (for example Vodafone) this can lead to their usage also being billed to your account.  If you suspect this, be sure to contact your ISP and have it sorted out.

--------------

This is obviously not a complete list yet, so I invite feedback so it can be improved :) The goal being making it a sticky and/or a PeterReader response for high usage.