I am looking to replace the wheels and tires on my 2006 Ranger. They currently have the OEM 15x7 wheels and matching tires. I want to go up to a size 16 rim, but I am not sure how wide my truck can handle. I would like to go to 16x9, but hesitant to buy without getting some feedback. What do you think?

 

The width of the rim you use has more to do with the off-set of the rim, the back spacing of the rim.

Read here: The Ford Ranger/Bronco II Wheel Fitment Guide To Measuring Wheels

You can use longer studs or inset lugs and spacers if your rims have too much off-set, too deep.

This will give you clearance for turning lock to lock without rubbing, but they may stick out too far passed the edge of the fenders.
Judgement call on your part.

Diameter of tire is also a factor, read here: Ford Ranger / Bronco II Tire Fitment

This is the overall height of the tire you use, not related to rim size, but is related to fitment.

So if your current tires are 29" tall and the new tires are also 29" tall then you just have the back spacing to deal with

Also using the same overall tire diameter will keep speedometer accurate, taller or shorter tires will change speedometer and odometer readings

 

Tire Rack shows many rims with 16x8 and 16x7 to choose from. none of their wheel and tire combinations that they show would require modifications to your truck.

 

I would personally go with 16x8, lots of folks felt they are better wheels. Check out this thread for comments:

https://www.ranger-forums.com/wheels...7-16x8-119443/