Here are the steps to add a property to the table designer in SQL Server Management Studio. The steps involve altering the values in registry settings.

NOTE: Please be careful while altering registry keys.

• Type regedit in the Windows Start --> Run command to open the Registry Editor.
• Navigate to HKEY_CURRENT_USER\Software\Microsoft\Microsoft SQL Server\100\Tools\Shell\DataProject
• You might need to change the SQL Server version accordingly. I am using SQL Server 2008 R2 Express and hence the version 100. For SQL Server 2012, I found this setting under HKEY_CURRENT_USER\Software\Microsoft\SQL Server Management Studio\11.0\DataProject
• Under the above mentioned registry path, look for the keys SSVPropViewColumnsSQL70 and SSVPropViewColumnsSQL80 .
• By default, these registry keys will have the values 1,2,6; . Section Property sequence mentioned below shows the number associated with each property. For my requirement to add Description column to the table designer, I had to change the registry key values to 1,2,6,17;
• Right-click on the key and select Modify option. Change the value from 1,2,6; to 1,2,6,17;. This has to be done on both the keys SSVPropViewColumnsSQL70 and SSVPropViewColumnsSQL80
• NOTE: Remember to restart SSMS between each registry change.

Property sequence:

1. Column Name
2. Data Type
3. Length
4. Precision
5. Scale
6. Allow Nulls
7. Default Value
8. Identity
9. Identity Seed
10. Identity Increment
11. Row GUID
12. Nullable
13. Condensed Type
14. Not for Replication
15. Formula
16. Collation
17. Description

Hope this helps someone.

For those of you looking for a .REG file to achieve this, copy/paste these lines into a text file with a .REG extension. Double click that to add it to your registry. The column numbers are listed in the answer by pithhelmet . The example below uses "14.0" meaning the version of SSMS that started being released as a standalone tool from SQL 2017 onwards. I expect that the registry path will continue to stay at 14.0 for some time yet, even with regular updates for SSMS being released.

Windows Registry Editor Version 5.00

[HKEY_CURRENT_USER\Software\Microsoft\SQL Server Management Studio\14.0\DataProject]
"SSVPropViewColumnsSQL70"="1,2,6,3,7,8,17;"
"SSVPropViewColumnsSQL80"="1,2,6,3,7,8,17;"

Note that you need to have SSMS closed when you apply these changes to the registry.

For SQL Server Management Studio Version 18.x (2019) and 19.x: First Close SQL Server Management Studio. then open Regedit and go to: "Computer\HKEY_CURRENT_USER\Software\Microsoft\SQL Server Management Studio\18.0_IsoShell\DataProject" and then Change the SSVPropViewColumnsSQL70 and SSVPropViewColumnsSQL80 Data from 1,2,6; to 1,2,6,17

For SQL-Server-Management Studio 2014 (SSMS 2014) it's a bit tricky to get the "Description" column (17):

1. Open SSMS 2014, wait for Login-Dialog is shown. (Don't click "connect"!)
   

2a) Open Regedit, goto: "HKEY_USERS\S-1...###YOUR-WINDOWS-USER-SID###-\SOFTWARE\Microsoft\SQL Server Management Studio\12.0\DataProject"

2b) Change the keys: SSVPropViewColumnsSQL70 and SSVPropViewColumnsSQL80 from 1,2,6; to 1,2,6,17;

3. Now click "Connect" at the SSMS 2014 Login-Dialog.