I use oil analysis, not so much to extend intervals, but to perform a check-up on the vehicle. It is roughly analogous to getting blood work done when you have a physical. Especially if you pay a pro like Terry Dyson to analyze the results.

You can gain early detection of fuel delivery problems, head gasket problems, air filtration issues and check the oil to see if it is a good match to your engine and driving conditions.

Me personally, I recommend at least one analysis at some point (well after break-in) to determine a baseline, then one every couple years or 30-50,000 miles as a check (unless you have reason to think there is an issue). Many an engine has been saved an early death by a $20 oil analysis when that analysis came back with the dread hi Si (air filtration leak) or showing water/glycol/Na (coolant leak).

My $0.02

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2009 VW TDI Jetta Sportwagon 172k miles (rear-ended harder than Elton John on 8/4/13. Total loss)

1991 Volvo 240 142k miles (T-boned by a stop sign runner. Total loss)