[Galaxy S III Mini General] xd.bx:
Great post, and very useful advice. Other partitions can be backup up as well in the following way:

cd /storage/extSdCard
mkdir backup
cd backup
dd if=/dev/block/mmcblk0p1 of=mmcblk0p1
dd if=/dev/block/mmcblk0boot0 of=mmcblk0boot0
dd if=/dev/block/mmcblk0boot1 of=mmcblk0boot0
dd if=/dev/block/mmcblk0p2 of=mmcblk0p2
dd if=/dev/block/mmcblk0p3 of=mmcblk0p3
dd if=/dev/block/mmcblk0p4 of=mmcblk0p4
dd if=/dev/block/mmcblk0p5 of=mmcblk0p5
dd if=/dev/block/mmcblk0p6 of=mmcblk0p6
dd if=/dev/block/mmcblk0p7 of=mmcblk0p7
dd if=/dev/block/mmcblk0p8 of=mmcblk0p8
dd if=/dev/block/mmcblk0p9 of=mmcblk0p9
dd if=/dev/block/mmcblk0p10 of=mmcblk0p10
dd if=/dev/block/mmcblk0p11 of=mmcblk0p11
dd if=/dev/block/mmcblk0p12 of=mmcblk0p12
dd if=/dev/block/mmcblk0p13 of=mmcblk0p13
dd if=/dev/block/mmcblk0p14 of=mmcblk0p14
dd if=/dev/block/mmcblk0p15 of=mmcblk0p15
dd if=/dev/block/mmcblk0p16 of=mmcblk0p16
dd if=/dev/block/mmcblk0p17 of=mmcblk0p17
dd if=/dev/block/mmcblk0p18 of=mmcblk0p18
dd if=/dev/block/mmcblk0p19 of=mmcblk0p19
sync

This will backup everything excluding the boot, recovery, system, cache, hidden, and data partitions. For the record, here is the PIT partition table:

--- Entry #0 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 1
Partition Flags: 2 (R/W)
Unknown 1: 1
Partition Block Size: 0
Partition Block Count: 256
Unknown 2: 0
Unknown 3: 0
Partition Name: MBR,GPT
Filename:

--- Entry #1 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 2
Partition Flags: 2 (R/W)
Unknown 1: 1
Partition Block Size: 256
Partition Block Count: 768
Unknown 2: 0
Unknown 3: 0
Partition Name: MasterTOC
Filename: STE_boot.bin

--- Entry #2 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 70
Partition Flags: 5 (R)
Unknown 1: 1
Partition Block Size: 1024
Partition Block Count: 2048
Unknown 2: 0
Unknown 3: 0
Partition Name: PIT
Filename: goldenxx.pit

--- Entry #3 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 71
Partition Flags: 5 (R)
Unknown 1: 1
Partition Block Size: 6144
Partition Block Count: 2048
Unknown 2: 0
Unknown 3: 0
Partition Name: MD5HDR
Filename: md5.img

--- Entry #4 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 3
Partition Flags: 2 (R/W)
Unknown 1: 1
Partition Block Size: 8192
Partition Block Count: 1024
Unknown 2: 0
Unknown 3: 0
Partition Name: STEboot1
Filename: STE_boot1.img

--- Entry #5 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 4
Partition Flags: 2 (R/W)
Unknown 1: 1
Partition Block Size: 9216
Partition Block Count: 1024
Unknown 2: 0
Unknown 3: 0
Partition Name: STEboot2
Filename: STE_boot2.img

--- Entry #6 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 5
Partition Flags: 2 (R/W)
Unknown 1: 1
Partition Block Size: 10240
Partition Block Count: 1024
Unknown 2: 0
Unknown 3: 0
Partition Name: Dnt
Filename: dnt.ssw

--- Entry #7 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 6
Partition Flags: 2 (R/W)
Unknown 1: 1
Partition Block Size: 11264
Partition Block Count: 1024
Unknown 2: 0
Unknown 3: 0
Partition Name: reserved
Filename:

--- Entry #8 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 7
Partition Flags: 5 (R)
Unknown 1: 1
Partition Block Size: 16384
Partition Block Count: 2048
Unknown 2: 0
Unknown 3: 0
Partition Name: CSPSAFS
Filename: cspsa.img

--- Entry #9 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 8
Partition Flags: 5 (R)
Unknown 1: 1
Partition Block Size: 18432
Partition Block Count: 2048
Unknown 2: 0
Unknown 3: 0
Partition Name: CSPSAFS2
Filename: cspsa2.img

--- Entry #10 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 9
Partition Flags: 5 (R)
Unknown 1: 5
Partition Block Size: 20480
Partition Block Count: 32768
Unknown 2: 0
Unknown 3: 0
Partition Name: EFS
Filename: EFS.img

--- Entry #11 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 10
Partition Flags: 5 (R)
Unknown 1: 5
Partition Block Size: 53248
Partition Block Count: 32768
Unknown 2: 0
Unknown 3: 0
Partition Name: ModemFS
Filename: modemfs.img

--- Entry #12 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 11
Partition Flags: 5 (R)
Unknown 1: 5
Partition Block Size: 86016
Partition Block Count: 32768
Unknown 2: 0
Unknown 3: 0
Partition Name: ModemFS2
Filename: modemfs2.img

--- Entry #13 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 12
Partition Flags: 5 (R)
Unknown 1: 1
Partition Block Size: 118784
Partition Block Count: 102400
Unknown 2: 0
Unknown 3: 0
Partition Name: Fota
Filename: ssgtest.img

--- Entry #14 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 13
Partition Flags: 5 (R)
Unknown 1: 1
Partition Block Size: 380928
Partition Block Count: 128
Unknown 2: 0
Unknown 3: 0
Partition Name: IPL Modem
Filename: ipl.bin

--- Entry #15 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 14
Partition Flags: 5 (R)
Unknown 1: 1
Partition Block Size: 385024
Partition Block Count: 28672
Unknown 2: 0
Unknown 3: 0
Partition Name: Modem
Filename: modem.bin

--- Entry #16 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 15
Partition Flags: 2 (R/W)
Unknown 1: 1
Partition Block Size: 417792
Partition Block Count: 4096
Unknown 2: 0
Unknown 3: 0
Partition Name: Loke4
Filename: normal.bin

--- Entry #17 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 16
Partition Flags: 2 (R/W)
Unknown 1: 1
Partition Block Size: 421888
Partition Block Count: 4096
Unknown 2: 0
Unknown 3: 0
Partition Name: 2ndLoke4
Filename: normal2.bin

--- Entry #18 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 17
Partition Flags: 5 (R)
Unknown 1: 1
Partition Block Size: 425984
Partition Block Count: 32768
Unknown 2: 0
Unknown 3: 0
Partition Name: PARAM
Filename: param.lfs

--- Entry #19 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 18
Partition Flags: 5 (R)
Unknown 1: 1
Partition Block Size: 458752
Partition Block Count: 32768
Unknown 2: 0
Unknown 3: 0
Partition Name: Kernel
Filename: boot.img

--- Entry #20 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 19
Partition Flags: 5 (R)
Unknown 1: 1
Partition Block Size: 491520
Partition Block Count: 32768
Unknown 2: 0
Unknown 3: 0
Partition Name: Kernel2
Filename: recovery.img

--- Entry #21 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 20
Partition Flags: 5 (R)
Unknown 1: 5
Partition Block Size: 524288
Partition Block Count: 2457600
Unknown 2: 0
Unknown 3: 0
Partition Name: SYSTEM
Filename: system.img

--- Entry #22 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 21
Partition Flags: 5 (R)
Unknown 1: 5
Partition Block Size: 2981888
Partition Block Count: 1720320
Unknown 2: 0
Unknown 3: 0
Partition Name: CACHEFS
Filename: cache.img

--- Entry #23 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 22
Partition Flags: 5 (R)
Unknown 1: 5
Partition Block Size: 4702208
Partition Block Count: 655360
Unknown 2: 0
Unknown 3: 0
Partition Name: HIDDEN
Filename: hidden.img

--- Entry #24 ---
Unused: No
Partition Type: 2 (EXT4)
Partition Identifier: 23
Partition Flags: 5 (R)
Unknown 1: 5
Partition Block Size: 5357568
Partition Block Count: 9891840
Unknown 2: 0
Unknown 3: 0
Partition Name: DATAFS
Filename: userdata.img