Though ordinary 99-cent furnace filters catch about 75% of bulk dirt, they capture very little (often less than 3%) of minute pollutants. So, these furnace filters are not likely to help with allergies unless they are changed very frequently and your primary allergy is to larger particles, like some dust particles.
Slightly more effective than regular furnace filters are treated furnace filters. These disposable products, which typically sell for under $10, have been coated with dirt-trapping glycol or mineral oil. While they stop about the same percentage of bulk dirt, these furnace filters may also block up to 10% of the smaller, microscopic particles.
Many people consider HEPA furnace filters to be the "gold standard" of filters. HEPA (High Efficiency Particulate Air) filters have the capability of trapping extremely small particles, including those less than 1 micron in diameter. This represents an extremely high filtration capability. HEPA units are usually constructed with a pre-filter of some type so that the HEPA filter does not become quickly clogged with larger particles. This type of filtration system can be quite expensive. Typically, the pre-filter will need to be replaced yearly and the HEPA filter every two or three years. This can be a significant expense.
You can get HEPA replacement filters for your air conditioning and furnace systems. These filters are a simple substitution for the filter you are using now. The disadvantage is that the air in your home will only be filtered when one of these two systems is 'running' and the fan is on. There is also no pre-filter to trap larger particles, so you could be changing filters more frequently. The advantage is that you can often just add these filters to your existing system, with no new equipment needed. Check with your owner's manual, if in doubt.
Much more effective than standard furnace filters (with almost HEPA effectiveness) are the electronic furnace filters or electrostatic air filters. Most of these models work with central forced hot air or an air conditioning filter, but these units are permanent (as opposed to the disposable standard replacement furnace filters for a home). You can expect a higher initial cost for the greater effectiveness and for the fact that they are built to deal with your whole home.
Some furnace filter models are electric and will cost a little more to keep them charged. While these furnace filters may not handle smoke removal accurately, they can come up with "HEPA-like" filtering capabilities for small 1-micron particles in the air.