You're going to get a wide range of opinions on this. Many people adamantly believe that Android is immune to viruses, and will tell you that antivirus apps are useless and just use up CPU and battery. I'm no tech security expert, but I do know that hackers and cybercriminals are some of the most creative people in the universe, and it's just a matter of time before Android malware becomes a big threat. So I always recommend staying ahead of the curve and installing a well-respected security app like AVG as mentioned above, or my choice, which is Lookout. Do a Google search on Android security or Android antivirus, and look for articles in established tech sources like PCMag or PC World, and read those reviews. Then give a number of them a try to see how your device performs while they're installed. I settled on Lookout because (1) it consistently gets high marks from known tech reviewers, (2) it doesn't suck battery according to my battery stats, and (3) I don't notice any effect on performance as long as scheduled automatic scans are turned off.
The other benefit of almost every Android security app is some option for remote wipe or location, although this might require payment. I've read a few recent stories of successful device recovery after it was stolen, thanks to security apps.