ICICI Bank, HDFC Bank, Axis Bank, SBI Bank, PNB, CitiBank - How Safe these Banks are?

Safety of a bank depends upon Two key ratio’s :

Capital Adequacy Ratio

Non-Performing Assets Ratio

Also, to be feel more safe- Spread your Deposits.

Look at the banks' key ratios and parameters (such as net worth and profits). This will tell you about its financial health.
Capital Adequacy Ratio: Commercial banks need to maintain a minimum capital to risk-weighted assets ratio (CRAR) of 9 per cent. In simple terms this means that if the bank has given out Rs 100, it should have at least Rs 9 with it as capital.
Here's a brief snapshot of the CAR of some banks:

Private sector banks*	CAR (In per cent)
ICICI Bank	13.97
HDFC Bank	13.60
Axis Bank	13.73

Public sector banks*	CAR (In per cent)
State Bank of India (SBI)	13.53
Bank of India	13.01
Punjab National Bank	13.10

Foreign banks*	CAR (in per cent)
Citibank	12
Standard Chartered	10.59
HSBC	10.59

Non-performing Assets (NPA) Ratio: A non performing asset or a loan is when the interest and/or installment of principal on it has remained 'past due' or unpaid -- for more than 90 days. NPAs refer to the loans given by a bank that it classifies as doubtful. This means that the bank has low or no hopes of recovering money on these loans.
This gives a peek into how the bank uses its money for lending. Low NPAs mean that the bank has been prudent in giving out loans.

Private sector banks	Net NPA (In per cent)
ICICI Bank	1.55
HDFC Bank	0.47
Axis Bank	0.42

Public sector banks	Net NPA(In per cent)
State Bank of India (SBI)	1.78
Bank of India	0.52
Punjab National Bank	0.96

Foreign banks	Net NPA(in per cent)
Citibank	1.23
Standard Chartered	1.04
HSBC	0.58

Spread your deposits:
Deposits up to Rs 1 lakh are insured under the government's Deposit Insurance and Credit Guarantee Corporation (DICGC).
As per this scheme, even if you keep multiple deposits (savings and fixed deposits) across branches of one bank, only a total of Rs 1 lakh is insured.
There is another good news. The government is in talks with the RBI to raise the ceiling on deposit insurance from the present Rs 1 lakh to Rs 2 lakh.

Thats the simple logic of keeping your investments and deposits safe.