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Not unless you're downloading apps from shady sources. Otherwise, you generally don't have to worry about it. Any reports of viruses or malware you hear about is most likely from an app that was NOT in any official app store and was downloaded from one of those pirated app websites.
Also, be sure to check what permissions an app is asking for before you download it. If you're not comfortable with what you see or it doesn't make sense (e.g. a wallpaper app that asks permission to send SMS messages), don't download it.
This news article says that over one million phones in China were hit with a virus that sent spurious text messages without the users' knowledge, resulting in millions of dollars in losses.
I'm not aware of any Android viruses, but there are several rootkits available to Android hackers that will let you dig into your system to change stuff under the hood. Most people who do this aren't malicious, but it's apparently not that difficult to break into Android if you're a talented programmer.