I have a '99 Acura 3.0CL with 36K miles and excellent running condition. Yes, little old lady. Should I have the timing belt replaced as my mechanic suggests?
If plan on keeping it yes.
It can lead to a bad day not only a break down at any time but also $2k-3k in repairs. Call around for quotes, if a mechanic has not done a Honda V6 timing belt something is wrong.
Yep, it’s time and miles that wear them out, you’ll want to see what other services you might need at 12 years, check the manual.
It’s rubber. Remember those old pencils whose erasers got really hard and then didn’t work? Like that, but imagine that eraser holding your engine together. Replace it. It’s far easier than replacing the engine.
Like texases, check the manual. Likely there may be more. Sorry… 
Replace the belt. I recommend them at 10 year intervals if the mileage hasn’t been reached.
Think of it this way: If you brought your car in for routine t-belt replacement and the mechanic said “Hey, I found this belt in the back, It’s brand new, still in the box, but 12 years old” would you want that one installed on your car?
Remember the movie “Grease” ? What happened to the rubber thingy Kenickie kept hidden in his wallet? Remember folks . . . rubber ages and the possibility of breakage increases with that age. Change it now and move on. Rocketman
I’ve Never Seen "Grease."
Kenickie Kept A Spare Timing Belt In His Wallet ?
CSA
It sounds like you don’t follow the instructions in your owner’s manual for some reason. That’s not a good idea.
If the belt breaks, you’ll be spending a few thousand dollars for an engine repair or replacement. I’d strongly suggest replacing the belt now. Just so you know, it’s typical to replace the water pump and a few other parts at the same time, because the labor is already paid for and the parts are cheap.
I hope you have kept a record of all the maintenance that you have had done on this vehicle. Your mechanic should have recommended that you have the belt changed about 5 years ago. If you had it done then, you would not be doing it now, you would be doing it two years from now.
The belt is due for replacement every 7 years or 105k miles, which ever comes first.
Thanks for all the helpful comments. My trusty mechanic replaced the timing belt and water pump, automatic adjuster, air filter and a couple of belts. Total bill $850. Now I can start saving again for the next major service due in 10 years. 
End of discussion.
Not really. A timing belt should be replaced long before the 10 year mark and this is especially true if the engine is an interference fit. (Meaning if the belt breaks the engine will suffer major damage.)
If your car has an interference engine changing it wasn’t a bad idea. I own a '97 Ford Escort with 32K miles on it and it still has the original timing belt, but mine is a non interference engine meaning the pistons and valves won’t clash if the belt breaks. I just changed the timing belt on my '02 Escort a couple weeks ago at 9 years old and about 115K miles.