My fiance is 45 years old and has the following retirement plan at her
current job.  Each year she works, an additional 1.65% of her annual
income will be paid to her for the rest of her life, starting at age 65.
In other words, if she earns $50,000, for every year that she completes
at work she will get another $825 of annual income for the rest of her
life, starting at age 65.

She is thinking of switching jobs to a company that does not offer a
retirement plan.  She won't lose benefits she has already accumulated.
My question:  What is her retirement "worth", in other words how much
extra salary would she need without a retirement plan to "break even"
with her existing retirement plan?

Perhaps an equivalent question is:  at age 45, how much would an
annuity cost (paid for in full) that will guarantee $825 per year of
lifetime income, starting at age 65?

I don't know that the market expectations, risks, costs, etc of market
annuities- but if you want some math that might get you close, take a
look at using excel.

Assuming:
Life expectancy of 95 years (starts paying out at start of age 65 for 30 years)
and an interest rate of 5%

You plug those into the PV function in excel and you get a value of
$12,682 - that is the value of a 30 year annuity that would pay out
$825 a year for 30 years at 5% interest

Take the 12,682 (cost at age 65) - and assume that to buy it now at
.05% interest, it would cost about $5,000.($4,800) - again use the PV
function with a future value of 12,682 at 5%
 
So you have to make some assumptions but you can guess about 5k a year
with the above assumptions.