I was in atlanta for 4 months on L1 visa. My wife joined me after 3 months on L2 visa.I have social security number but my wife did not applied for it. Question : Do I need my wife's SSN for filing my tax returns in married status ?

If you were in the U.S. for 4 months, then you will file nonresident tax return. On nonresident return, you can not claim your wife.
You can claim travel expenses (includes transportation, lodging and meals) for the 4 month period. Use Form 2106 or 2106-EZ to figure your allowable expenses that you claim on line 9 of Schedule A (Form 1040NR).

BOTTOM LINE: Your wife does NOT need either a SSN or a ITIN, because she CANNOT be claimed as a dependent on your tax return.