I ride my bike to work. But every time I get a flat tire, my schedule is messed up because bike shops are not easily available on my town.
Is there any other option besides puncture-proof tires?
Over the years I've dealt with a variety of puncture inducing issues ranging from desert thorns to broken glass to nails and tacks and metal shards. While I agree with the other replies here that you shouldn't expect a puncture proof tire, there are some things you can do. Below are some of the tips and tricks that I have picked up over the years. The best answer for you is going to depend on what kind of bike you are using.
Start with a high quality, puncture resistant tire. I know you asked for other options, but a quality tire can make all of the difference. The Schwalbe Marathon Plus HS 440 is easily the most puncture resistant tire that I have ever used. I have arrived at work with ~50 desert thorns stuck into these tires without losing any air. More details available here: http://www.schwalbetires.com/bike_tires/road_tires/Marathon_Plus_HS440. Less industrious options (that are more suitable for road bikes where weight may be a concern) include the Continental 4000s and Continental GatorSkin tires.
Ensure that your tires are properly inflated. And double check the pressure at least weekly.
Inspect and replace your tires frequently. When your tires get too thin, they are more prone to punctures. While there is no exact science as to when you should replace a tire, I tend to do it sooner than later and have found that this significantly reduces the number of flats that I get.
Consider using a sealant inside your tubes. This is a liquid that will help to patch small holes in your tube as punctures happen. The two leading options here are Slime and Stans. Slime is thicker and is sold both pre-installed in a tube and separately (for injection into any tube). Stans is thinner and only sold separately (as far as I know). You can use an inexpensive syringe kit to inject the sealant into a tube through the valve stem. As a tire rotates the sealant will disperse throughout the tube. In the event of a puncture, the air rushing out is mixed with sealant, which results in the puncture getting patched on the fly. When it works properly, you might only lose a small amount of air and not even have to get off your bike. Of course you should replace that air when possible. And, depending on the size of the puncture, you may opt to replace that tube soonish as well. Typically Slime is recommended for lower pressure tires whereas Stans works well in higher pressure tires, due to the tradeoffs inherent with the thickness of each sealant.
Finally, when I was living the the US Southwest with lots of desert thorns, some people used a setup they liked to call "the system". This involved taking an old tire and cutting off the bead. Then installing this old tire between your tube and your new tire. The second layer of rubber provides a powerful barrier against punctures. Of course, it is also heavy and a large pain to install. I'd suggest that this is somewhat extreme, but I know people that love it so I figured it was worth mentioning here.
After taking all of these precautions, you should always carry the parts and tools needed to change a flat. With luck, the suggestions above will significantly reduce your need to use such items. But, it is always better to be prepared. Again, depending on your bike you may want to carry 1 or more tubes, a portable pump, tire levers, CO2 cartridges, a tube patch kit (I personally don't like these because I find that getting a good patch is often a game of chance, but some people love them), and some nitrile gloves.
Unless you can find solid rubber tires for your bike, there really is no such thing as a puncture proof tire. You can get tires that are more resistant to puncture, but they can and will still go flat- just not as often.
Why do you need a bike shop to fix a flat tire? You can easily do it yourself. All you need is a small saddle bag for tools and:
Changing the tire yourself is fairly easy. See: Changing a bike tire Use your spare tube so you don't have to take the time to patch a tube.
You might also want to include:
The additional tools above let you do other routine on-the-fly repairs and adjustments. The patch ket comes in handy if you have 2 flats in one day, OR get a larger cut in your tire- you can patch the actual tire itself (from the inside). The hex tool lets you adjust set height, straighten your handlebars, etc.
I can fix a flat front tire in under 10 minutes, and a rear tire in less than 15 minutes. Way faster than finding a bike shop.
Other answers and comments have covered the "toughen up" approach pretty well. Here are two techniques you can use:
It is not meant to be condescending, but watch where you're going. On your commutes this is easier said than done, because your main attention needs to be on the traffic for safety. But if you see glass or other trash on the road you can try to avoid it, by going 'round it, or bunny hopping over it (not if you have panniers). And if you are seeing trash in the same area repeatedly, you can search for a cleaner route.
On a road bike, if you know you have run over some trash, brush your tires with your hand. Most punctures occur by the tire "picking up" a sharp object, then hammering it through the tire by repeatedly hitting it on the road as the wheel rotates. While I have never hurt my hand doing this, it makes sense to wear cycling gloves. You'll almost never even know if there was anything to brush off. Of course, if your bike has mud-guards this option is a non-starter.
How to brush your tires
For safety make sure you only brush your tires at a point where the tire is moving away from the forks and brakes!
Front tire: While continuing to ride, reach down to the top of the front tire in front of the fork, and gently put part of your hand (I use the part between my thumb and first finger) against the moving tire. You do not need to press, just touch it as it brushes past your hand; that's sufficient to dislodge any trash adhering to the tire. Make sure you brush for at least two turns of the wheels.
Rear tire: the technique is the same, but it's a bit harder to do. Most people need to look where they are putting their hand, because it is easy to poke fingers into the moving spokes (it hurts)! Put your hand against the moving tire in front of the back-stay, but close to it. Keep well away from the down-tube: there is usually insufficient gap between the tire and down-tube for your hand, so getting your hand there hurts too.
Brushing your tires will not stop all punctures, but it does stop most. For 5 years of commuting I rode my touring bike (it has mud-guards) and would get punctures like everyone else. Then I switched to my road bike on the same route and same level of attentiveness to where I was riding, and the punctures fell to six in ten years (including one week when I had 3) and 50,000 km (30,000 miles).
What type of bike are you riding, and what width are the tires? Looking at the answers, the only thing I don't see is a reference to the width of tires. Narrow road bike tires get more flats that wider hybrid or trail bike tires. When I was commuting on a road bike I was using Bontrager Hard Case and tire liners and still got too many flats. Of course what constitutes "too many flats" varies from person to person, but when I changed to a hybrid (keeping the same type of tire set up, except wider [32mm]), my problems ended.