I agree with what has been said here - i.e. do exactly what they say or else they may use it to reject your claim.
Note that the large majority of rebates do not require original receipts;
they allow photocopies. Always follow the instructions, and you should be fine.
UPC codes is another story...
With respect to UPC codes, you need to send the original most of the time.
The unwritten rule of thumb in most cases, when multiple rebates are offered for a single product, is to send the original UPC in for the manufacturer sponsored rebate and to send the copy of the UPC code for the store sponsored rebate(s). HOWEVER, I always
follow the exact instructions for a given rebate.
The rule of thumb is just a guideline. Always, follow the instructions first, and when in doubt contact the rebate center...
I know I am repeating myself here, but it is for emphasis
Keep copies of the receipt, the rebate form, the UPC code, and if necessary (i.e. for a rebate that seems like it might be pulled, or where is doubt that multiple rebates will be honored), keep a copy of the product page or ad showing/mentioning the rebates.
After sending the rebate,
keep an eye on it. Many places offer online tracking.
If it isn't showing up within 4 weeks, call the rebate center. You might be asked to reasubmit the claim.
If you don't follow up on time, the promotion might be closed by the time you do look into it, and then it gets harder to get your money back, because they will have to issue a check from a special account, if it is even possible. It depends how hard you try, and which rebate center is involved.