If you have an older computer and can not get flash videos to play on sites like youtube, etc. it may be because the latest adobe flashplugin for linux is not compatible with your CPU. The solution is to downgrade the flashplugin version to one that is compatible.

(NOTE: To avoid possible typos or other mistakes, best to copy/paste commands listed here into the terminal.)

First, to confirm that this is indeed the problem, open a terminal (Menu -> Accessories -> Terminal) and enter the following:

inxi -f

You will see something similar to this:

CPU:    Quad core AMD Phenom II X4 B55 (-MCP-) cache: 2048 KB
    Clock Speeds: 1: 2100.00 MHz 2: 800.00 MHz 3: 800.00
    MHz 4: 3200.00 MHz
    CPU Flags: 3dnow 3dnowext 3dnowprefetch abm apic clflush
    cmov cmp_legacy constant_tsc cr8_legacy cx16 cx8 de
    extapic extd_apicid fpu fxsr fxsr_opt ht hw_pstate ibs
    lahf_lm lbrv lm mca mce misalignsse mmx mmxext monitor
    msr mtrr nonstop_tsc nopl npt nrip_save nx osvw pae pat
    pdpe1gb pge pni popcnt pse pse36 rdtscp rep_good sep
    skinit sse sse2 sse4a svm svm_lock syscall tsc vme wdt

Look at the "CPU Flags" portion of the output and look to see if it contains "SSE2".  If you only see "SSE", then your CPU needs to use an older version of the flashplugin.  If you do see "SSE2", then your problem is something else -- so don't bother with these instructions.

Another option is to look for "SSE2" in output of this command:

cat /proc/cpuinfo | grep --color=always -i sse

Once confirmed that your CPU requires an older flashplugin, you need to find out which flashplugin packages are currently installed and get rid of them.  To find out what is installed enter this into the terminal:

dpkg -l | grep flash

Your output will look like this, but the packages listed may be slightly different:

ii  mint-flashplugin                            2011.10.19                                all          Metapackage for Adobe Flash plugin
ii  mint-flashplugin-11                         11.2.202.280                              amd64        Adobe Flash plugin 11

Make note of each package name shown (package names will appear right after each "ii" in output).  These are the packages that need to be purged from your system.  They may be different from the ones shown in my example, so make sure to use YOUR package names in the command below to purge them from the system.  To purge the packages from your computer:

sudo apt-get purge mint-flashplugin mint-flashplugin-11

If, after hitting enter, it tells you that a few other packages will be removed as well -- accept that and enter "y" to continue with the purge.

Now that the incompatible flashplugin packages have been removed, you need to install an older version that will be compatible.  To do that you have two choices: install the latest "old" version that is known to work by downloading it directly from Adobe's site; or use Synaptic Package Manager and install from there an older version that is a little older than the one from Adobe's site.  (Why the latest "old" one from Adobe is not available in Synaptic, I don't know.  But I can confirm from my own testing that either one of the two will work.)

Before proceeding, you will need to know whether your Mint installation is 32-bit or 64-bit architecture.  To find out, enter this in the terminal and look at info for "Kernel":

inxi -S

For latest flashplugin from Adobe's site:

-- Use this link to download flashplugin zip file:  http://fpdownload.macromedia.com/get/flashplayer/installers/archive/fp_11.1.102.63_archive.zip
-- Choose to "Save" file and point it to save in your Downloads folder.
-- After download completes, open your file manager and navigate to the Downloads folder.
-- Right-click on the zip file and choose "Extract here"
-- Double-click to open the extracted folder
-- Now look for the folder for either 32-bit or 64-bit to go with your system and double-click to open it.  (Note: ignore the one with name ending in "debug".)
-- Now, for 32-bit systems look for the one ending in "linux.i386.tar.gz"; for 64-bit systems, "linux.x86_64.tar.gz".
-- Right-click the one for your system and choose "Extract here".
-- Double-click to open the newly extracted folder for it and you will see a folder and a file named "libflashplayer.so"

The "libflashplayer.so" file is what you need.  That file needs to be copied into the correct place into the file system to get flash videos working.  For this tutorial, I'm specifying the placement for Firefox browser.  If you use a different browser, check to see if it has a directory under the same /usr/lib location and try same steps as listed here.

If you know how to use the terminal to do this, cd to the location of the libflashplayer.so file and "sudo" copy it to /usr/lib/mozilla/plugins.  Otherwise....

To copy that "libflashplayer.so" file into the proper directory you will need to do so as the root administrator.  So, open your file manager again.  Now right-click on your Downloads folder and select "Open folder as root".  (Be careful now; as root you can do damage to the system if you make a mistake.)

Now, navigate your way through the folders you extracted until you get to the "libflashplayer.so" file.
-- Right-click on the file and choose "Copy"
-- Now navigate to the /usr/lib/mozilla/plugins directory and paste the file inside it.

(If you are lost, click "File System" on the left pane of your file manager program to get to the starting point of "/"; then look for and double-click to open the "usr" folder; then the "mozilla" folder; "plugins"; then in the right pane, right-click and choose "paste" to paste the "libflashplayer.so" file into the "plugins" folder.)

-- You're Done!  Close out the file manager.  Open Firefox and videos should work now.

SEE ADDITIONAL NOTE BELOW.



To Use Synaptic Package Manager (If you have a 64-bit system, use the above method for a more compatible driver.  This one might work, but performance will be better with the other one):

(EDIT added 12/28/13 -- As ByeByeXP noted in comments section yesterday, it appears that older versions of the flashplugin are no longer available to choose from in Synaptic as of Mint 16.  If you are using Mint 16 or higher, use the proceedure for downloading older plugin directly from Adobe's site.  Hopefully, that option doesn't dissappear also.)

-- Open Synaptic (Menu -> Administration (or System) -> Synaptic Package Manager).
-- Hit the "Reload" button and wait for it to finish updating itself.
-- In the Quick search box, type "flashpl"
-- From the results listed, select mint-flashplugin-10.3; click the empty box to the left of the name and choose "Mark for Installation".
-- Click the "Apply" button and wait until it completes.
-- When install completes, click on the line for mint-flashplugin-10.3 again to highlight it.
-- Now, along the top of Synaptic, click "Package" and choose "Lock Version".  This will prevent future system updates from changing the flashplayer back to the newer version.
-- Your done!

ADDITIONAL NOTE:  When you first go to video sites and try to play videos, they may complain that you need to upgrade your flashplayer.  DO NOT do that.  Simply click the circle with the line through it on the video player window and tell it to allow use of the older player and remember that setting for the site you are on.  Repeat that procedure for each site you run into asks you to upgrade the player.

EDIT added 12/28/13 -- Note that using an older flashplugin may introduce possible security vulnerability issues.  Although more so on Windows than Linux, the risk is not zero -- so, you may want to keep the plugin deactivated in your browser when not using it for video viewing.

EDIT added 10/14/2014 -- Changed original inxi command to one that gives fuller output of cpu flags and gave alternative command for those using distros that do not have inxi command installed.  (austin.texas in Mint forums pointed out that sometimes inxi -C may not show flags as I expected on some CPUs.)

Sources of info used for this tutorial:
http://helpx.adobe.com/flash-player/kb/archived-flash-player-versions.html#Flash
https://wiki.debian.org/FlashPlayer/
http://forums.bodhilinux.com/index.php?/topic/8593-get-flashplayer-working-on-old-computers-under-bodhi-23/
http://forums.linuxmint.com/viewtopic.php?f=47&t=138535&start=20#p768945
http://forums.linuxmint.com/viewtopic.php?f=90&t=149361#p783079
http://forums.linuxmint.com/viewtopic.php?f=90&t=148882#p779756