Secure keyboard application from android market Is it safe to install a keyboard application from android market that asks full internet access permission? Will it not lead to certain security risks?

There are several free and paid keyboards that are very popular with millions of downloads. Some of them asks that permission while others do not. What is the difference?
It's definitely a valid concern and you should be wary of apps that can record keystrokes with "Full Internet" privileges.

It's best to reach out to the developer of such keyboard app and ask them this question directly.  I imagine such a permission would be required for something benign, like downloading language packs (from within the keyboard app) or showing ads, for example.