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For logging into ebay paypal banking and the like. Thanks
Assuming you've not installed a rogue application, (rare but we had a brief breach recently),
On your ISP's network, as secure as their network, ie very.
On a public WiFi connection, as secure as their network, ie not at all.
On your own WiFi connection, as secure as your network, who knows.
Does that mean I need anti-virus software on my smart phone?
If so, which is best?
No, it doesn't.
It means that, when you install an Android app from an unknown source and it presents you with a list of the privs it wants, you should check what it's asking for. If you're installing a Bejewelled type game and it wants access to your address book and the GPS receiver, you might want to say 'no'.
You don't need AV for phones, the only people who'd have you believe that are AV sellers. You just need to either install from known-good publishers or check what access you're granting when you're installing the "Paris Hilton Farts" application.
Cheers