I enjoy singing, and I want to improve. I've had an ear for music since I was very young, and I have no problems finding/matching/hearing a tune in my head. However as I've gotten older, I've found it increasingly difficult to sing a note that I can hear in my head. I guess my voice has just changed over time, making it harder to reach notes that I once could. I feel very limited and constrained vocally. What exercises/techniques can I practice to broaden my vocal capabilities and reach my potential?
The best advice I can think to offer is for you to find a vocal instructor in your area and begin studying with them. Based off the information in your question, it seems as though you are trying to sing material inappropriate for your voice type. Working with a trained vocalist will not only give you the pedagogical tools you need to develop and refine your vocal production, but will provide information about what type of voice you have and what sort of material you should be performing.
Myself or someone else providing suggestions exercises would only serve as a quick-fix and would be doing you a disservice.
Potentiality increases over time as your technique and knowledge improve. In order to succeed at the best possible level, I'd suggest long-term work by studying with a voice instructor (not a "vocal coach" unless their credentials offer appropriate merit.)
I realize that this answer is probably not the one you were looking for, but I think it is one that needs to be offered.
Hope that helps.
I agree with jjmusicnotes. He has very good points to offer.
If you are willing to spend some money on practicing your craft I recommend Brett Manning's Singing Success click here for the website. His work is truly amazing and he has help me increase my range by a full octave. It has also helped my style tremendously.
If you can not afford his program then I recommend doing lip rolls (look up videos on how to do lip rolls) on a comfortable scale. Do that daily and then start to increase the pitch of the scale slowly moving upward (you can do it down in pitch too). Along with the lip rolls make sure you sing daily. Practice singing your favorite songs, but never over do it! You can harm or hurt your voice if you strain it or sing too much and too long.
With that said have fun and keep singing!