How do I remove a Linode from my account?

Here’s how:

Log in to the Linode Manager.

--> To remove a Linode from your account, click the Linodes tab, and then select the Remove link next to the Linode you want to remove.

--> To remove extras from your account, click the Linodes tab, select a Linode, click the Extras tab, and then select the Remove link.

--> To remove a NodeBalancer from your account, click the NodeBalancers tab, and then select the Remove link next to the NodeBalancer you want to remove.

--> To remove the Linode Backup Service, go to the Backups tab in your Linode’s Dashboard, and click the Cancel Backups link at the bottom of the page.

Update:
You can either click on the Linodes tab on the sidebar on the left just like the previous solution. On the right side of your Linode, you will find "…" three dots which acts as a menu and gives you the option to delete the Linode among other things.

You may also click on the Linode itself, go to the Settings tab, then click on Delete. I guess it was too easy to remove or delete them before, and this is to prevent any accidental deletion. :)

To add to @biennino's instructions, we have a guide for Removing Services that lists the following steps:

1. Log into your Cloud Manager.
2. Select "Linodes" from the sidebar links.
3. Select the Linode you would like to remove, then select the "Settings" tab.
4. Expand the "Delete Linode" panel and click "Delete".

There is an alternative way for deleting Linodes from your account as well:

1. Log into your Cloud Manager.
2. Select "Linodes" from the sidebar links.
3. Click the ellipsis (three dots) to the right of the Linode in question.
4. Select "Delete" from the bottom of the menu.

Our Cloud Manager has been updated since the original answer was posted, so the instructions are a bit different!