How to safely turn off swap permanently and reclaim the space? (on Debian Jessie)

1. If you have GParted open, close it. Its Swapoff feature does not appear to to be permanent.

2. Open terminal and become root (su); if you have sudo enabled, you may also do for example sudo -i; see man sudo for all options):

   sudo -i
   

3. Turn off the particular swap partition and / or all of the swaps:

   swapoff --all
   

4. Make 100% sure the particular swap partition partition is off:

   cat /proc/swaps
   

5. Open a text editor you are skilled in with this file, e.g. nano if unsure:

   nano /etc/fstab
   

6. Comment out / remove the swap partition's UUID, e.g.:

   # UUID=1d3c29bb-d730-4ad0-a659-45b25f60c37d    none    swap    sw    0    0
   

7. Open a text editor you are skilled in with this file, e.g. nano if unsure:

   nano /etc/initramfs-tools/conf.d/resume
   

8. Comment out / remove the previously identified swap partition's UUID, e.g.:

   # RESUME=UUID=1d3c29bb-d730-4ad0-a659-45b25f60c37d
   

9. Don't close the terminal as you will need it later anyway.

Note: The next steps differ depending on, whether you rely on CLI or GUI.

---

GUI:

1. Open up GParted, either from menu, or more conveniently from the terminal we have opened:

   gparted
   

2. If you don't have it installed, you may do so; afterwards run the previous command again:

   apt-get install gparted
   

3. Choose your drive from top-right menu.

4. As the GParted reactivates the swap partition upon launch, you will have to right-click the particular swap partition and click Swapoff -> This will be applied immediately.

5. Delete the swap partition with right click -> Delete. You must apply the change now.

6. Resize your main / other partition with right click -> Resize/Move. You must apply the change now.

7. Back to the terminal, let's recreate the boot images:

   update-initramfs -u -k all
   

8. Update GRUB:

   update-grub
   

9. You may reboot now if you wish to test that the machine boots up.

---

CLI:

I will check in VMs if my solution works, then I will share it. In the meantime, see this answer.

Execute as root:

# swapoff -a

And to make that change permanent, edit /etc/fstab and remove or comment-out the swap entry.

Comment/remove the relevant entry in the /etc/fstab to prevent it from being reenabled on the next boot, then reboot or run swapoff -a to disable the usage of the swap partition for the currently running system.

Now delete the swap partition, extend your system partition over that unused space and extend the actual filesystem. I don't know whether your graphical partition manager can do all that, but if it can't here's a distro-agnostic way of doing this using fdisk and resize2fs :

# fdisk /dev/sdX

# Display current partition table, copy/paste this output somewhere to be able to go back in case you screw up

Command (m for help): p
Device       Boot  Start    End Sectors Size Id Type
/dev/sda1        2048  22527   20480  10M ef EFI (FAT-12/16/32)
/dev/sda2       22528 186367  163840  80M 83 Linux
/dev/sda3      186368 204799   18432   9M 82 Linux swap / Solaris

# Delete the swap partition

Command (m for help): d
Partition number (1-3, default 3): 3
Partition 3 has been deleted.

# Delete the system partition

Command (m for help): d
Partition number (1,2, default 2): 2
Partition 2 has been deleted.

# Create a new system partition starting the same as the old one but ending a bit farther, at the end of the (now deleted) swap partition

Command (m for help): n
Partition type
   p   primary (1 primary, 0 extended, 3 free)
   e   extended (container for logical partitions)
Select (default p): 

Using default response p.
Partition number (2-4, default 2): 
# Enter the same start sector as the old part.
First sector (22528-204799, default 22528): 22528
# Enter the end sector of the old swap partition
Last sector, +sectors or +size{K,M,G,T,P} (22528-204799, default 204799): 204799

Created a new partition 2 of type 'Linux' and of size 89 MiB.

# Save the changes
Command (m for help): w
The partition table has been altered.

Finally we extend the current filesystem to make use of the new free space (until now the actual filesystem wasn't aware that we added some more space to its underlying partition). By default, resize2fs uses the entire partition unless a fixed size is given, so we don't have to specify anything other than the partition block device. Growing a file system (as opposed to shrinking) can be done online with the partition mounted :

# resize2fs /dev/sda2

Now you've successfully disabled swap and reclaimed the unused space without even rebooting.

Note that the procedure for Debian is a bit different and requires editing some more files. Check out this answer for more info.