I live in the United States with the green card. I gave a talk at some university, I didn't charge for it but they agreed to reimburse the 50 USD I had paid for renting a car. They asked me to fill a W9 form. Do I have to declare these reimbursed 50 USD when filling my tax forms?
This is by no means authoritative tax advice, but my understanding is that typically this is not taxable income.
I'm having a hard time finding official information on what happens when you are reimbursed by an organization that is not your employer. But IRS Pub 463 describes travel reimbursements for employees and independent contractors. The general idea, as I read it, is that if:
the reimbursement is for reasonable travel expenses (car rental is pretty normal);
the university has an "accountable plan" (which they almost certainly do);
you submit an accounting of your expenses (e.g. your receipts);
your reimbursement does not exceed the amount of your submitted expenses
then the reimbursement is not taxable income. It won't be reported as income to the IRS, and you won't get a 1099-MISC nor W-2. I have been in your exact situation many times and these conditions always applied.
So, why did you have to fill out a W-9? My experience is that almost any university has a standard "vendor payment" system that they use for all payments to non-employees. As part of the standard vendor registration process, they always ask the "vendor" to submit a W-9, just in case they should ever make a taxable payment to that vendor. For academic visitors, typically no taxable payments will be made, so the form is never actually relevant, and was just meaningless paperwork.
The only common exception is that in some cases, the university might pay you an honorarium or speaker fee, in addition to your travel reimbursement. An honorarium is taxable income and needs to be reported as such, probably on the "Other Income" line of Form 1040. You will only receive a 1099-MISC if the payment exceeds $600, but you have to report it whether you receive a 1099-MISC or not.
(An unfortunate side effect is that the university collects your social security number, even though they don't really need it for anything. If you keep this up for long enough, you'll sooner or later get a letter from some university you visited years ago, regretting to inform you that some database containing your SSN was hacked, and that data may or may not now be in the hands of some villain. If you're lucky they might offer to pay for a subscription to some worthless credit monitoring service for some inadequate period of time.)
The common sense reason for reimbursed expenses not being taxable is because the transactions you are being reimbursed for were (usually) paid for with after-tax dollars.
For example, if you use your debit card to pay for a car rental, the funds in the corresponding bank account are most likely from your income, which was already taxed. The purchase itself will also have already had any applicable sales tax included in the transaction, so you will have already paid that too. The reimbursement is simply to make you whole, there is no need to tax you a second time on either the net income used to pay for the goods/services or the sales tax. (Side note - this is the same logic used by credit card companies when they give you "cashback" - it's not interest income because they are simply "refunding" a portion of a purchase that you'll be paying for with post-tax dollars).
If you have received any funds in excess of expenses incurred then a W-9 would be required, as now it would count as compensation, not just restitution. The university may just have a standard practice of requesting W-9s for all payments made, and then later on reconcile which transactions will be reported as income vs expense reimbursement. Might be worth asking them if they intend to report this payment as taxable income or not.
If you have receipts in an amount equal to the reimbursement and you do not receive a 1099 from the university, then it has not been reported to the IRS and there is really no reason for you to declare it on your return. However, if you do receive a 1099, rightfully or wrongfully, then it's already been reported to the IRS and at that point it is probably worth saving yourself any hassle with the taxman by just declaring it as income. (At typical income tax rates this is not going to add very much to your tax bill).
The company then uses the information you provide on the form to prepare Form 1099-MISC, reporting to the Internal Revenue Service the amount of income it paid to you or your company.
If you do receive a 1099-MISC, you could also file a Schedule C-EZ with your tax return and show the $50 as an expense to off-set the income, and will therefore have no tax liability.