The answer to your question basically depends on the medicine you are referring to.  Most asthma inhalers should be tossed after a year, as the chemical composition changes over time.  When I find inhalers that have been lying around for a while, I notice they taste funny and don't work as well.  Of course you will want to keep one around in case of emergencies, but you should toss out the old one and renew the prescription at least once a year. I personally lose inhalers all the time, so I make sure to date them when I remove them from the box just in case.

As for other asthma medications, it is best that you discuss with your pharmacist when your medications are set to expire and should be tossed out and refilled.