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Usually I find a flight I like that uses one or more connections with the same or different companies. In these cases, if the distance between the first and the second connection is not too large, I prefer to go by bus or train and then take the flight. The problem is that sometimes it is more expensive to take the flight in the second airport than to take the flight from the first one. I mean, I'm wondering why sometimes it is more expensive to take only a flight than to take the same flight and another one.

A practical example (and real, you can check with SkyScanner). Imagine I am in Madrid (Spain) and would like to go to Rio de Janeiro (Brazil) on April 1st. The cheapest flight I have found is this:

TAM airlines: MAD -> GRU -> GIG : 507 €

Fantastic! GRU is one of São Paulo's airports. That's perfect for me! I'll go on to Rio traveling overland. But then, I look for this flight (MAD -> GRU, non-stop):

TAM airlines: MAD -> GRU : 597 €

It's the same flight, 90 € more expensive! I've found this kind of behavior a lot of times and I'm intrigued to know why it happens.

I think the answer has to do with competition.

If you want to fly from Madrid to Rio de Janeiro with one stop, you have lots of options. You can fly TAM (via Sao Paulo), TAP Portugal (via Lisbon), American (via New York or Miami), KLM (via Amsterdam), Air France (via Paris), etc, etc. (I found these with Kayak.) There is a lot of competition and this will tend to drive fares down.

However, if you want to fly from Madrid to Sao Paulo nonstop, your only choices are TAM, Iberia, and (somewhat surprisingly) Air China (though only twice a week). There is less competition, so fares may tend to be higher, and this may exceed the effect of the cost of the extra flight GRU-GIG.

As a more exaggerated example, from my home airport of Ithaca (ITH), I've often seen ITH-EWR-SFO (a total of 4400 km) priced lower than ITH-EWR (which is only 275 km). There are three different airlines providing one-stop service ITH-xxx-SFO, but only one that flies ITH-EWR nonstop.

This effect is why hidden city ticketing can sometimes be advantageous, and why airline policies usually forbid it.

Not just competition, but also supply and demand. Many people prefer direct connections for their convenience, and are willing to pay more for them. Also, the separate legs of the indirect connection may well be less busy routes, requiring the airline to lower prices on those legs in order to entice passengers who'd otherwise either not travel or take other modes of transport (e.g. airfare between Amsterdam and Paris fell sharply when the high speed rail link was started).

You have to weigh the cost difference against the time loss and inconvenience (plus the higher risk of mislaid or stolen luggage).

It could be the time of day. Often red-eye flights are cheaper, or business-hour flights are more expensive. The MAD -> GRU one could be a really convenient and popular flight, and as such they can charge more for it, while the MAD-> GRU -> GIG one may be leaving at 4am and arriving at an awful time as well, but it's convenient for them to relocate planes then or something, so they offer a lower price to fill the plane.

In addition, landing charges may vary at different times of the day, to get a spot in the queue or at the terminal during peak times will cost more.

Airports charge the airlines quite a bit for premium slots :)

The most comprehensive and direct answer is “because the airline figured they could sell one of this seats at a higher price”. Time of day, convenience, competition, costs all figure in what's acceptable to the passengers and whether the airline can stay in business but none of this directly dictates price.