The biggest thing, given that you already claim your wife-to-be as a dependent, is that the tax tables you will use will change. If you work and your wife-to-be does not, then by switching from "single" to "married" you will be taxed at the lowest possible rate, in addition to still being able to claim your wife and son as dependents.
For example, say your yearly taxable income is $50k. Filing "Single" for the 2011TY with no credits, you would owe $8,631 in taxes. Filing "Head of Household" (as you should do as a single parent) and all other things equal, you'd owe $7,274. Filing as "Married Filing Jointly" (which is what you should do for a one-income household), you'd only owe $6,654.
Something to be aware of: As of 2011, there is very little "marriage penalty" for two roughly equal earners (worst I can find is still within $10 compared to filing single, almost literally a rounding error), and thus there is a pretty large "marriage advantage" for disparate incomes (including single-income households), as shown above. If the Bush-era tax cuts expire on those making less than $250k/yr and taxes return to 2001 levels, starting in the 2013TY you'll end up paying about what you do now as a single earner (so no "marriage advantage"), and in addition if your spouse worked and made about the same as you, you'd see a hefty "marriage penalty" whether you filed jointly or separately. This is a big chunk of the looming "Taxmageddon" that Republicans are screaming about (without doing much other than blaming Obama, when he can't even do anything without Congress making up its damn mind). Another one that would impact the Average Joe/Jane is the expiration of the current AMT threshold increase, meaning if your taxable income from the normal method of computation is over $48k, you will owe the AMT (basically paying a flat 26% on income without your standard deduction or personal exemptions). The last chunk is the payroll tax cut given to employers, which you don't see on your paycheck per se but can definitely affect your ability to get and stay hired, as your employer will consider that into the cost of hiring you or keeping you.
BTW, if you have been the primary wage earner for yourself, your wife and your son for a significant time (years) and have not been filing as HoH, I would be filling out amendments (1040X) for every year in which you could have claimed HoH status; as I showed above, the IRS could owe you a big chunk of change for every year you were HoH and didn't file that way.
Other than that, other big financial changes are the combination of credit histories; your credit history will reflect on your spouse and vice versa. Now, it's possible to get around that in the first few years. My wife and I were able to buy a house based on my credit score alone by putting all the paperwork in my name, without listing my wife as "co-owner". My wife, being my wife, still has legal joint ownership of it, but we didn't have to figure her history into a combined credit score (the flip side being we didn't get to count her income, so our pre-approval amount was based on what I could afford to pay, which was in hindsight a very good thing as we ended up pregnant 4 months later and she no longer works). But, after a few years of combined financial transactions, most of that goes away; you'll be joint accountholders on most of your deposit/investment accounts and lines of credit, etc.
The last big one is that she, and not your son or your parents, will become your next of kin. Your son (probably a minor) is too young to make financial or legal decisions, but as of right now before you marry your girlfriend, your son will inherit your estate, and it will likely be placed in trust to your parents. From the moment the marriage license is certified by the officiator (priest, pastor, JP), your wife will become your next of kin and, barring a last will and/or advance directive to the contrary, will have final say over your care and/or control over your estate should you be incapacitated or killed.
Depending on your relationship with each other, not a whole lot else will change. I found that with my wife not working after she became pregnant with our new daughter, she became the de facto accountant for our finances simply because she has the time to do it. With most of our bills set up to be paid automatically (initiated by us via "bill pay", not on auto-debit), it's relatively easy to track, and if she weren't there it would be a five-minute exercise on my part each payday to plan for the next four weeks' worth of bills and savings.