Mostly just the usual stuff:

Evidence of regular maintenance (oil changes, etc.).
Smooth shifting transmission.
Heat and A/C that work properly.
Accelerates, steers, and stops straight.
No rattles or clunks in the suspension.
No check engine light.
No peculiar noises.
Power windows and door locks all work properly.
Seat heaters work.
Seat mechanicals work as they should.
Sunroof opens and closes properly and doesn't leak.
If AWD, get it on a dirt road and make sure front AND rear wheels spin under hard acceleration.
Two key fobs. Purchasing and programming one will cost about $500. (Forget what you read on ebay about getting a key on the cheap. It doesn't work that way.)

They're good cars. Solid as a brick S/H. Given how much they weigh, they have plenty of umph and get pretty decent gas mileage. We just sold our 2005 2.5T FWD and purchased an almost-new S60 Inscription. Although the S60 is a very nice car, it doesn't have that solid Volvo feel the way the S80 did.

Good luck.
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Current rides: 2018 Volvo S60 Inscription (What the heck do all these buttons do?), 2005 Volvo S80 2.5T (Soon to go bye-bye), 2003 Volvo V70 2.4NA (The family "truck"), 1973 Volvo 1800ES (STILL not road worthy!)