How to fix "sudo: unable to open ... Read-only file system"?

The filesystem will usually go into read-only while the system is running if there is a filesystem consistency issue. This is specified in fstab as errors=remount-ro and will occur when a FS access fails or an emergency read-only remount is requested via Alt+SysRq+U. You can run:

sudo fsck -Af -M

to force a check of all filesystems. As one of the other answers states, looking at dmesg is also very helpful.

Edit: Don't forget the -M on the command-line.

NOTE: As mentioned by Bibhas in his answer: If fsck gets stuck after its version banner:

$ sudo fsck -Af -M
fsck from util-linux 2.20.1

you may want to try using the EXT4-specific fsck

$ sudo fsck.ext4 -f /dev/sda1

Provided the partition in question /dev/sda1 was an ext4 filesystem.

The answer by hexafraction didn't work for me. Every time I tried executing sudo fsck -Af -M it just showed

$ sudo fsck -Af -M
fsck from util-linux 2.20.1

and nothing else. No error or anything. For me, booting into a live disc and executing this worked -

sudo fsck.ext4 -f /dev/sda1

Provided the partition in question /dev/sda1 was an ext4 filesystem.

Here is the command that solved my problem :

mount -o remount /

better than a reboot or sudo fsck -Af