If I were you I would pay off these loans today. Here are the reasons why I would do this:
For car loans in particular, it's much better to not pay interest on a loan since cars lose value over time. So the longer you hold the debt, the more you end up paying in interest as the car continues to lose value. This is really the opposite of what you want to do in order to build wealth, which is to acquire assets that gain value over time.
I would also recommend that once you pay the loan, that you set aside the payment you used to make on the loan as savings for your next car. That way, you will be able to pay cash for your next car, avoiding thousands of dollars of interest. You will also be able to negotiate a better price by paying cash. Just by doing this you will be able to either afford to buy a nicer car with the same amount of money, or to put the extra money toward something else.
For the student loan, 3% is a very low rate historically. However, the reason I would still pay these off is that the "return" you are getting by doing so is completely risk free. You can't often get this type of return from a risk-free investment instrument, and putting money in the stock market carries risk. So to me, this is an "easy" way to get a guaranteed return on your money. The only reason I might not pay this down immediately is if you have any other debt at a rate higher than 3%.
General Reasons to Get out of Debt
Overall, one of the basic functions of lifetime financial planning is to convert income into assets that produce cash flow. This is the reason that you save for retirement and a house, so that when your income ends when you're older these assets will produce cash, or in the case of the house, that you will no longer have to make rent payments. Similarly, paying off these debts creates cash flow, as you no longer have to make these payments. It also reduces your overall financial risk, as you'd need less money to live on if you lost your job or had a similar emergency (you can probably reduce your emergency fund a bit too). Discharging these loans will also improve your debt-to-income ratio if you are thinking of buying a house soon.
I wonder whether as someone who's responsible with money, the prospect of cutting two large checks feels like "big spending" to you, even though it's really a prudent thing to do and will save you money. However, if you do pay these off, I don't think you'll regret it.