MIL-STD-188-110D defines a 38,400 baud modem at 48 kHz bandwidth. With 256QAM, the raw data rate is 240 kbps.
Of course, the 2.8 kHz bandwidth rule prohibits that in the ham bands. The FCC had originally declined to set a maximum bandwidth in their first ruling, but that caused everyone's head to explode (and that's one of the reasons this ruling has taken so long).
The HF ham bands aren't very wide. With the exception of 10 meters, from 50 to 500 kHz wide. Folks (including the ARRL) were afraid of abuse. With an SDR, you can generate a signal with any bandwidth you desire.
The reason the FCC didn't want to set a limit is because it's arbitrary. For example, MIL-STD-188-110D (which is an open standard) has a 2400 baud 3.24 kHz mode. But now it's illegal.
Taking the 2.8 kHz bandwidth limit into account, around 2000 to 2400 baud depending on the excess bandwidth of the root-raised-cosine filter used to shape the signal.
The bandwidth of a single carrier signal is symbol rate * (1 + RRC excess bandwidth). A typical excess bandwidth is 0.35, so 2000 syms/s * 1.35 = 2700 Hz.
You can use a tighter roll-off, like 0.2. 2400 syms/s * 1.2 = 2880 Hz. Unfortunately, the tighter roll-off increases the PAPR (Peak to Average Power Ratio) of the transmitted signal.
Your comment is 100% technically correct, except that people reading it may think that baud means numbers of bits per second.
If you have more than 2 possible symbols, you can do much more than that; 256QAM could be getting 8 bits/second/Hz under very strong signal conditions.
This theorem states that the theoretical maximum channel capacity ("bandwidth" as measured by bits per second) is dependent on analog bandwidth (the other "bandwidth" lol) and signal to noise ratio.
Now that's the information theoretical maximum, but stuff like QAM as people mentioned, and other more advanced techniques like OFDM and "next layer" stuff like FEC can get you very close to the theoretical maximum.
I used to dialin to Pine (and Lynx) at 1200bps. If I remember correctly, I could read about as fast as the words came to screen. If you're just saving for reading later, 5kbps is tons for email.
It's really hard to do on modern operating systems. Too many services that will dogpile a low bandwidth link once they see that a network adapter is up.
Of course, the 2.8 kHz bandwidth rule prohibits that in the ham bands. The FCC had originally declined to set a maximum bandwidth in their first ruling, but that caused everyone's head to explode (and that's one of the reasons this ruling has taken so long).
http://tracebase.nmsu.edu/hf/MIL-STD-188-110D.pdf