Basmati rice is one of the lower ones on the GI index (50s)(though some quickcook brands are quite high)
Oddly I can't find a brown basmati on the database;
Wild rice is also in the 50s.
All rice becomes much higher in gi when cooked until very soft.
Personally I use a mixture of basmati, brown and wild cooked until its only just lost the 'bite'. Whatever the gi the gl is relatively high since all rice has a high proportion of carbohydrates. portion size is crucial.
(technical points
The gi of rice seems to depend on the amount of amylose (a type of starch) content. Some rice vaieties are reported to be really high amylose and have low gis, there's one from Bangladesh with a GI of 27 but unfortunately these aren't easily available. Basmati is a sort of medium amylose rice. Brown rice isn't necessarily much lower on the index but is far better nutritionally than white rice. Some of the sticky rices like jasmine are very low in amylose and are faster than glucose with gis over 100.
According to the gi database, Uncle Bens converted parboiled rice mixtures...at least those sold in the US and Canada seem to have relatively low gis.. I think it's something to do with the manufacturing process producing resistant starch)
edited to correct