Clicking Safari brings up the launch screen for Safari and then it immediately quits. Double clicking the Home button shows Safari is still running. Quitting it and restarting does not help. Quitting and restarting phone does not help.
It's because I jail broke the device with a tethered jailbreak. A tethered jailbreak requires you to use the jailbreak software (viz., Redsn0w) to boot the device (the option "just boot tethered") whenever it is turned off (hence "tethered").
If I don't boot the phone with the jailbreak software, Safari doesn't work (along with some other default applications). All my fault.