I have had success cleaning my camera's sensor myself. Of course, I cannot guarantee that it will work out equally well for you, and if you're unsure, by all means consult a professional service lest you ruin your camera. But this is what works best for me so far:
I bought lint-free cleaning tissues, and everytime I clean my sensor, I tie one of them to the end of a thin, soft and flexible rubber tube, connect the other end of the tube to a vacuum cleaner and set the cleaner to lowest power. Then I carefully wipe the sensor with the tissue, applying next to no pressure for fear of scratching the surface, and the cleaner sucks away any bits of dust that come loose. If you're unsure about the vacuum power, connect the tube to the cleaner very loosely to lessen the suction power at the front end of the tube even further.
There are people who suggest using a brush instead of the tissue; possibly this works as well, though I imagine a brush bringing in additional dust under normal room conditions (i.e. no clean-room).
Anything else I tried (using a tissue without the vacuum cleaner attached, or using fluid) just ended up redistributing the dirt across the sensor, or even glueing it to the surface.