Remember back in the late nineties when all sorts of kooks were trying to warn us about the brain-melting dangers of cell phone radiation? Back then we couldn't find any proof positive of such dangers, so we ignored them and made fun of the crazy people. Well, today those nuts get vindication. Gizmodo reports that, according to the Environmental Working Group, long-term cellphone use is associated with a higher tumor risk.
If you still use an old feature phone, you're probably fine. The ten lowest-risk mobile phones were the Samsung Impression, Motorola RAZR V8, Samsung SGH-t229, Samsung Rugby, Propel Pro, Gravity, the T-Mobile Sidekick, LG Xenon, Motorola Karma, and Sanyo Katana II.
The increasingly ubiquitous smartphone, unfortunately, is the most dangerous type of mobile to use. Every model of iPhone puts out a big ol' dose of radiation (.52-1.19 W/kg for the 3GS). The Palm Pre and G1 also scored poorly, putting out .92 W/Kg and 1.11 W/Kg, respectively.
Does this mean you need to panic and dump your smartphone in the waste-bucket? Not exactly. You're probably fine browsing the Internet, texting, and chatting. Those activities keep the phone itself pretty far away from your brainmeats. For extra security, look into grabbing an earpiece or going with a bluetooth device.
It's still entirely possible that cell phones of all types are perfectly harmless and don't do a damned thing to cause tumors. Research is ongoing, and studies like this have been wrong many times before. This isn't the time to panic, but taking some basic precautions won't hurt anything, and could end up being very useful in the long run.