Assuming a Component input, then the main difficulty would be converting the YPbPr (luminance and colour) signalling into RGB. Such a task may be done in the analog domain, as is done on CRT TVs, or via digital signal processing.
Besides that, there is seperating the horizontal and vertical sync pulses from the Y channel, this is slightly trivial, as there are off-the-shelf parts that do this (Nat Semi, LM1881).
The horizontal sync frequency for 720p is well within the range of 17" CRT monitors. If one were successful in converting the component HD input into a RGBHV signal, then the picture will display, albeit probably stretched vertically. Whilst the analog CRT does not have any notion of "anamorphic stretching", you'll have to manually adjust the vertical size as close to the 16:9 ratio as possible, the limit being the monitor's range for the vertical sweep.
For LCD monitors, with analog VGA inputs you'll need to do the same as the above, except now you'd have to contend with the LCD's scaler unit. It's a mixed bag, some LCDs allow 1:1 (scaler off, centered image) but more often than not they don't.
With DVI, this is technically a non-issue, since timing and sizing information is embedded in the signal. However, HD content protection (HDCP), possible on HDMI, throws a spannar into the works.