What matters is how abused the additive package in the oil is. The more abuse it suffers the sooner you'll need to change it.
If all you do is drive short distances in town, somewhere around 3000 miles is a good estimate. But if you commute 50 miles a day on the freeway, then 7000 is a safe estimate. All that you're interested in is making sure that the detergent and anti-corrosion properties are still good enough to do their jobs. Once they are used up all you have left is the oil lubricating the engine. Without the additives you'll start seeing deposits and/or corrosion inside the engine.
There have been a few articles (available online - use Search on this forum to find references) that suggest that the GM Oil Life Monitor (OLM) is quite good at helping you determine the best time to change your oil. It's set up for regular oil, so if you switch to full synthetic then you'll be able to drive farther between changes.
When I bought my car I purchased the 3/36 LOF and tire rotation package (before knowing about the OLM), so I'm changing it every 3000 miles regardless. Once I get the last one at ~36K, I'm switching over to full synthetic as well and using the OLM. I believe that I'll end up changing it around 7-10 thousand miles. I'm at 15K now.
'11 LTZ, born Aug 2010, Fairfax, KS
V6/A6, Red Jewel Tintcoat / Cocoa-Cashmere, Sunroof
Mods: WeatherTech mats, CHMSL Pulser
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