In communication with interplanetary space probes, it is clear that one has to take the delay caused by speed of light into account. Besides that, what are current limits for the data upload and download bitrates? What is the main cause of the limit?
Speed-of-light delay is mostly irrelevant for data transmission rates. Once you get out of Earth orbit, transmissions are generally "fire and forget"; if data gets garbled, you schedule a retransmission of the garbled portion at a later time.
The limit for interplanetary communication rates is the Shannon limit: how fast you can send data while still being able to distinguish it from background noise. This in turn is influenced by antenna gain (a bigger sending or receiving dish lets you transmit faster), transmission power (a "louder" transmitter can send data faster), and distance (the further apart your antennas are, the more the signal fades towards background levels and the slower you can transmit).
Because of how many variables there are, there is no one "achievable bitrate". I wouldn't be surprised to find that Arecibo could talk to a counterpart in Neptune orbit at gigabit or even terabit data rates, while the Galileo probe's non-directional antenna could talk to the Deep Space Network antennas at only 160 bits per second from Jupiter.
If you want to see what sort of data rates are in real-world use, NASA's Deep Space Network status page will show you which probes are currently transmitting or receiving, and if you select "more details", it will tell you the transmission rate (for example, as I write this, antenna 15 at Goldstone is receiving data from MRO at 1.5 Mbps).
The highest bandwidth for any interplanetary mission is probably MRO, which at its peak can have a rate of 4.0 Megabits/ second, using the Ka band and at the closest point to Earth. I suspect that rate is contingent on the use of the larger DSN antennas, which are not always available, although I haven't done the math to confirm this.
If you count the Moon, the fastest is LRO, which can transmit at 100 Megabytes/ second, faster then most Ethernet connections! It can do this partially because it is closer, and partially because of the use of laser communication.
The limiting factor, as it is with most communications, is the signal-to-noise ratio. This can be improved in a number of ways. The easiest way is to increase the signal, which involves the use of directional antennas, which are typically larger then non-directional antennas. The signal gets weaker as the range goes up. Increasing the frequency will allow for more directional antennas, and generally speaking will lower the noise as well. This factors in to Shannon's theorem, which was mentioned in another answer.