Given that there is Android-based malware out there, and that so many good anti-malware apps are available for free, I think the clear answer is that yes, you should install anti-virus software on your device.
I don't believe in faith-based use of anti-malware software.
Here is information from AV-Test.org on the performance of "Anti-Malware Solutions for Android". The best ones (in terms of detection) were those offered by "Avast, Dr. Web, F-Secure, Ikarus, Kaspersky, Lookout, McAfee, MYAndroid Protection, NQ Mobile, and Zoner".
Some popular anti-virus apps performed horribly. I strongly recommend looking at
the PDF yourself.
Of course, good detection is essential, but it's only part of the picture. It's no good to have an app that offers strong detection if it makes your phone unbearable to use. So, I recommend reading the feature lists of the top-performing apps, reading reviews (the ones written by people who seem to be sane, anyway), and trying a few of the apps for yourself.
Some of these apps offer so-called "anti-theft" features, which might make them tempting to use. But keep in mind that there are also many dedicated anti-theft apps available, so you don't
have to get all the functionality you want in just one app (or from one developer, as the case may be).
Also, some anti-virus apps (Kaspersky Mobile Security Lite, at least)
only scan apps as they are being installed, and can't scan anything already on your phone.
I have personally been impressed with
avast! Mobile Security,
Dr.Web Anti-virus Light, and
Zoner AntiVirus Free. Each has its own strengths and weaknesses, though.
I hope that helps.