Do i delete my old W-2 forms from previous years?

Yes, you can delete the W-2's from last year that may show up in the W-2 summary, if you are no longer working for that company.

Use the 'delete' trash can next to the W-2 to remove.

How about for my current employer? 

If you wish to delete your current W-2, you can do so by following the steps in this TurboTax help article: How do I change my W-2 info in TurboTax?

@windseclib

What I mean is whether I can delete my prior year W-2 from my current employer. The other specialist said I can delete my prior year W-2 if it is from a previous employer I no longer work for. 

You may delete the W-2 entries that carried over from the previous year's tax return.

If need be, you will be able to access W-2 information from the previous year's tax return in Tax Home.  Follow these steps:

• Down the left side of the screen click on Tax Home.
• At the bottom of the page, click on Your tax returns & documents. 
• Select  Download/print return (PDF).
• Access your previous year’s tax returns to view tax information.

See also here.