Why is HDMI->DVI image sharper than VGA?

VGA is the only analog signal from the above mentioned ones so it's already an explanation for difference. Using the adapter can further worsen your situation.

some further reading: http://www.digitaltrends.com/computing/hdmi-vs-dvi-vs-displayport-vs-vga/

Assuming brightness,contract and sharpness are the same in both cases, there could be 2 other reasons why text is sharper with DVI/HDMI:

The first has already been stated, VGA is analog so will need to go through an analog to digital conversion inside the monitor, this will theoretically degrade image quality.

Secondly, assuming you are using Windows there is a technique called ClearType (developed by Microsoft) which improves the appearance of text by manipulating the sub pixels of an LCD monitor. VGA was developed with CRT monitors in mind and the notion of a sub pixel is not the same. Because of the requirement for ClearType to use an LCD screen and the fact that the VGA standard doesn't tell the host the specifications of the display ClearType would be disabled with a VGA connection.

Source: I remember hearing about ClearType from one its creators on a podcast for This().Developers().Life() IIRC, but http://en.wikipedia.org/wiki/ClearType also supports my theory. Also HDMI is backward compatible with DVI and DVI supports Electronic Display Identification (EDID)

The others make some good points, but the main reason is an obvious clock and phase mismatch. The VGA is analog and is subject to interference and mismatch of the analog sending and receiving sides. Normally one would use a pattern like this:

http://www.lagom.nl/lcd-test/clock_phase.php

And adjust the clock and phase of the monitor to get the best match and the sharpest picture. However, since it is analog, these adjustments may shift over time, and thus you ideally should just use a digital signal.

Another issue is a lot of VGA cables are junk. If the VGA cable is less than 1/4" thick, you will probably notice ghosting on larger monitors (Higher the rez, more likely ghosting). I've even noticed ghosting on the attached VGA cable on some 19" CRT montitors. My VGA cables are about 1/3" thick and it really helps with the sharpness (Thicker wires, more shielding)