Improving range is a goal for just about any trumpet player, and very few of us feel like we wouldn't want a couple more notes up from our current ability. Such improvement can help you be more confident in reading, try multiple chairs or parts and expand your horizons with new music. Progress is exciting! However, it should be approached with caution and planning, for many brass players have found that pushing your body too far can lead to injury and digression.
Say you were an athlete. How about a runner? If you wanted to improve your mile time, you wouldn't wake up one morning and decided to gain a minute. It doesn't work that way. Why would instrument playing be any different? If you need a new note for a concert or performance in a month, it probably won't happen, and the intelligent thing to do would be simply to give it to somebody with better range. However, progress can be made. If you decided to run faster, you would evaluate where you currently are, and set some goals. Writing down goals solidifies them as legitimate goals, and not just "wishes." Then, you would evaluate exercises and activities from knowledgeable sources and make a plan. You follow that plan, and you make progress. Such is the way that range improves.
Some good sources for range-improvement exercises include the studies by Bai Lin, James Stamp, Max Schlossberg, James Thompson, Cat Anderson, Carmine Caruso and several others. What works for one person may not necessarily work for another. Also, many university professors and qualified teachers can offer suggestions for exercises and can help you make a plan for progress. A private teacher is really a necessity for most musicians to progress. Even top-of-the-line professionals often seek advice from other professionals.
This thread is here to aggregate suggestions and advice, as well as collect stories of success and progress to motivate others. Please note that not all advice in this thread will work for you or is from a qualified professional, but such is the nature of the Internet anyway.