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Even though you may not owe tax, as a Resident Alien you are bound by the same rules as any US citizen, which is that you must report, and pay tax on, worldwide income.
Although there is a $ limit that if you make UNDER the amount (for single filers with no other dependents, you would not have to file a tax return if your income is below $9750.00)
You can find these limits on page 7 of http://www.irs.gov/pub/irs-pdf/i1040.pdf
However, under an H1B visa, it would be extremely unlikely for you to make less than $9,750.00
Additionally, if you had more withheld through your W2 than what your true tax liability is, then by not filing you will be giving up the right to claim that refund.
You have 3 years that are considered "open".
That means that you have 3 years from the due date of the return (plus extensions) in order to file your tax return and still be able to claim a refund .
After that time, the IRS will keep your money, even if you were due a refund.
How does this non filling affect my status?
Your status as in Resident Alien status?
Once you gain Residence Alien status, you keep that status until you either apply for a green card, or you decide to permanantly leave the US
Not filing does not change you're status
Ok. Thank you.