Copying the entire disc:

$ dd if=/dev/sr0 of=image.iso bs=2048 conv=noerror,notrunc iflag=nonblock

Where:
dd - the utility that will copy the media.
if= - input file.
/dev/sr0 - the CD or DVD ROM drive.
of - output file.
image.iso - image file name.
bs=2048 - means 2048 or 2 KiB block size.
conv=noerror - causes dd to continue after a read error.
notrunc - will avoid any automatic truncation of the output file.
iflag=nonblock - sets an "input flag" that causes dd to use non-blocking I/O, which should minimize the impact on your system at the possible expense of speed during the copy.

Sample output recovering a dual layer DVD:

dd: reading `/dev/sr0': Input/output error
1131104+0 records in
1131104+0 records out
2316500992 bytes (2.3 GB) copied, 396.483 s, 5.8 MB/s
dd: reading `/dev/sr0': Input/output error
2475273+0 records in
2475273+0 records out
5069359104 bytes (5.1 GB) copied, 1058.16 s, 4.8 MB/s

Recovering

Mount the image using the loopback driver:

# mkdir /mnt/mountpoint
# mount -o loop image.iso /mnt/mountpoint

Now you may cp or tar or burn it again into a DVD the files on /mnt/mountpoint.