You could. However, this would require other planets to intercept our communications from hundreds of light years away. We first have to make the assumption that we will long enough to meet the other people. To do this, we need to understand the levels of power that the other planets would need to receive in order to listen to us. For example, the Sun outputs 3.9x1026 Watts. A class C TV station can broadcast at 1x106 Watts. Thus, the sun is about 4x1020 times more energy intensive than a broadcast station. Converting the broadcast station to magnitude power, we get that the station has an absolute magnitude of about 56. Magnitude is a logarithmic unit used to measure the brightness of an astronomical object. Absolute magnitude is a measurement of an object at a distance of 10 parsecs, or about 33 light years. The sun has an absolute magnitude of 4.84.
According to Wikipedia, we can see the faintest object with Hubble at 32 magnitude. Comparing 32 magnitude to 56 magnitude, the broadcast station is about 4 billion times more dim than the dimmest signal that Hubble can receive. Say that we want to increase our distance to 100 light years. A 10 times increase in distance gives a 100 times decrease in power, due to the inverse square law. This would make our broadcast about 400 billion times more dim than is noticable, which means that there is no way in hell that the aliens would be able to notice us.
However, we have methods to improve this. For example, instead of using a radio tower, we managed to use the Deep Space Network to broadcast to this alien world, which has an antenna gain of 80dB, or about 100 million times the power concentration of a radio tower, we would still be shy by 4,000 times the level necessary for Hubble. Let's assume that the aliens have amazing telescopes, which are 10,000 the size of the hubble. This would give it a mirror size of 130 meters, which is about 13 times larger than the largest human telescope. According to section 2.3 of this paper, this telescope would cost more than $25 billion, not including the costs to put it into space, which assuming the telescope is 10,000 tons, at $10000 per ton, would cost on the order of $200 billion!
This would put us at 2.5 times above the noise floor, or about a 3dB signal to noise ratio. This is just fine for communications.
Note that this requires both us and the aliens to know about each other, and for us to know to point our telescopes at each other!