|These are all variants of the DVI connector. The same size of connector is used, but some pins may be present or missing, and some pins used or not used accordingly.|
DVI-I has the full set of analog and digital pins and signals. This is usually obvious by the presence of 4 pins by themselves with a think metal strip separating them into two pairs. A DVI-I cable is usually much thicker than DVI-D or DVI-A because is has more signals to carry. Not all computers and DVD players are DVI-I.
DVI-D has only the TMDS (transmission minimized differential signal) pins present, plus a few others. Such a connector or cable can only support digital data, which offers a higher quality than analog because it is far less susceptible to picture noise or image deterioration. DVI-D cables may be thin or thick depending on quality and whether they are Dual-link DVI or not.
DVI-A has only the analog pins present (4 pins by themselves with a think metal strip separating them into two pairs), plus a few others. No digital signal is supported, and the cable is usually quite thick, depending on its quality.
See also What is EDID?