It really depends.
Good or bad maintainence makes a difference and if you don't rinse your reg, 10 dives per year is more than enough to cause problems with a first stage. Similarly, one trip to the dunk tank without a tightly sealed dust cap and the reg will need to be serviced.
At the other extreme, in nearly all first stage designs, the high pressure seat is off the orifice when the regulator is unpressurized so no impression is made on the seat over time. This means that if properly stored, a first stage can have a very long shelf life. On the other hand, most of the wear in a first stage occurs at the seat and it is normally the part that will fail first, so the more dives you make, the more wear that will occur.
In contrast most second stages leave the soft seat in contact with the orifice and over time it can develop an excessive seating groove even if it has never been dove. This can be compensated for to some extent on a regulator with an adjustable inhalation knob, but eventually performance will suffer and inhalation effort will rise. How much this is a problem depends on any devices incorporated to lift the seat off the orifice during storage, the hardness of the seat and the strengh of the spring in the second stage. (As a general rule, if you have an inhaltion effort adjustment knob, back it all the way out during storage to reduce the pressure on the orifice.) Some designs, like the Scubapro D400 use a very light spring and a relatively hard seat so it normally takes years of storage for the seat to develop an excessive seating groove.
So what does all that mean in the real world? I do about 130 to 160 dives per year and when I used to do this with one regulator, it was about 50/50 whether I would need to service the reg somewhere between 100 dives and the end of the season as it was not uncommon for the first stage to develop intermediate pressure creep from a leaking high pressure seat. When I switched to doubles, and also started swapping roles for the primary and back up regs in mid season, the need to service the reg dissappeared.
So with poor rinsing and improper care, 1 year is way too long and 10 dives are way too many. With proper care and preventative maintenance 100 dives is acheiveable but the odds of a problem increase the more that number is exceeded.
If you have over 100 dives on your reg, it is probably not a great candidate to take along on a week long dive trip somewhere nice. If you are paying a couple thousand dollars for a dive trip, splurge and spend another $70-$100 on an annual service a month or so before the trip (and then dive the reg a time or two to make sure there are no adjustment issues.)
