EDIT: I understand leftovers with half dose, since some meds they can only give you a full bottle of. In that case, throw out the extra, because the meds break down and aren't as effective after a couple of weeks. I print out the list of covered prescriptions from my insurance company as well as the list of $4 medications from walmart and if possible, I try to have the doctor prescribe a lower-cost alternative. Walmart has amoxicillin for $4, but it's not always the best choice, so sometimes I do end up with a pricier medication. My mom was a stay at home mom with five kids and we never re-used medications, because even with some leftover, there wont be enough for a full dose for the full length of time.
If you are following the dispensing instructions, you should not have any leftover antibiotics. If you routinely have leftovers, then you are either missing doses, not giving the correct amount, or not giving the medication for the prescribed number of days.
I realize that with experience, some people can tell when their child will need an antibiotic. However, unless you're a doctor or an expert in pathology, just giving your child an antibiotic that you have laying around can do more harm than good because not all germs respond to just any antibiotic. Antibiotics are a formulation, and formulations break down over time, some more quickly than others. I wouldn't keep any medication past the expiration date, and with antibiotics, there shouldn't be any left to keep.
Just because the doctor prescribed amoxicillin for the last ear infection doesn't mean that s/he won't prescribe zithromax or something else for the next one, based on how much fluid is in the ear and how inflammed it is. Just because the doctor prescribed zithromax for the last respiratory infection doesn't mean s/he will prescribe it again. Germs become immune to antibiotics if they are given too frequently.
I am a single mom and understand money being tight. It seems my son always gets sick when there is $30 in the bank and a week or more until payday. I keep a low limit, low interest credit card for emergency use for this kind of thing - to pay the copays for the doctor visit and medications. If the medication cost is an issue consider filling them at Target or Walmart - they both have low-cost prescriptions, with many commonly prescribed drugs around $4. If the unexpected cost of a doctor visit is the issue, then try putting aside ten dollars a month just for that purpose and only use those funds towards unexpected doctor visits.
There have been many times that my own mother knew I needed an antibiotic (she had nursing training) but took me to the doctor so that the doctor could decide which antibiotic I needed. I leave it upto my son's doctor to decide whether he needs antibiotics - and sometimes he doesn't, because antibiotics only treat bacteria, not a viral infection.
The bottom line is you shouldn't have any leftover antibiotics to be worrying about using. Not giving the medication as often and for as long as prescribed can actually make the bacteria stronger and resistant to antibiotics. Make sure you are giving the dosage properly. Lastly, my mom gave me this piece of advice regarding food in the fridge but it works in the medicine cabinet too:
WHEN IN DOUBT, THROW IT OUT!