The biggest inroad I can think for a game company would be to befriend an interested teacher. Offer to come into a classroom or an after school program to demo one of the games. Come prepared with some sample lesson plans for the teacher to show how the game could directly address their particular state's standards.I want to agree with Ryan. This is the best way to get noticed by the teachers. A good time to do this is either at national conferences (although be forewarned that many of the larger conferences attract mostly administrators and college faculty because classroom teachers have a harder time getting released to attend conferences. I've only been able to attend ones that are local to me), or at teacher in-service days. I would bet that most districts have district-wide in-services on one day, and many also have special sessions for brand-new teachers. You could ask to attend those sessions by having a table set-up at one of the main locations with flyers or coupons, maybe a raffle to get a few games.
Speaking from experience when I began a Go program I had a few distributors donate some equipment to me. Later that year I got around 400$ from my school and spent almost the entire amount with those specific vendors. I also thank those vendors in my handout to the kids and our school website to try to give them some advertising back for their help.This tends to be what I do as well. If I've been treated well by a company, I'm going to go back to that company if they sell the product that I want to purchase. I will also recommend that companies' products to other teachers and friends. Like Ryan, I've been "gifted" with things based on proposals I've written. Some of the proposals were written when I was a pretty new teacher in the late 90s; of the companies that helped me out, I still purchase or use a lot of products from IntelliTools, and Attainment. On the other side, I had one company turn me down, and even now, I will often look at another company to see if they have the product available (there is a lot of crossover among educational publishers) in their catalog before going to the company that turned me down.