I decided to have a list of the banks I know in case you are thinking of options where to put your money/savings. I find this issue important in the sense that more or likely you will be doing hundreds to thousands of transaction with these banks for years.
Banco De Oro (BDO) [https://www.bdo.com.ph/personal]
Bank of the Philippines Islands (BPI) [https://www.bpiexpressonline.com/]
Metrobank [https://www.metrobank.com.ph/]
East West Bank [http://www.eastwestbanker.com/]
Philippine National Bank (PNB) [http://www.pnb.com.ph/]
Development Bank of the Philippines [https://www.devbnkphl.com/]
Union Bank [http://www.unionbankph.com/]
May Bank [http://www.maybank2u.com.ph/]
Land Bank of the Philippines [https://www.landbank.com/]
China Bank [http://www.chinabank.ph/personal.aspx]
Asia United Bank [https://www.aub.com.ph/]
Bank of Commerce [http://www.bankcom.com.ph/main.php]
MegaLink [http://www.megalink.com.ph/]
BancNet [http://www.bancnetonline.com/BancnetWeb/goToMainPage.do]
Since there are a lot more, I listed the ones that have been present for quite sometime now. And may be the ones that have a lot of branches and have good presence in many places. If you want your bank to be included, do not hesitate to email me.