Is it worth it to grow my own hops or should I just buy them somewhere?
Growing and using your own hops exclusively presents two definite setbacks in brewing: variety and proportions.
When you grow your own, you're generally limited to a single variety of hops which limits the hop flavors in the beers you make. Some hops contain a lot of alpha acids are are great as bittering hops (e.g. magnum), while others impart things such as citrus notes, spiciness, and great floral aromas. Buying hops gives you the ability to perfect your hop schedule by choosing additions that add different things to the beer.
Growing your own hops also means you'll be adding whole hops cones or whole leave to your beer rather than pelletized hops. This isn't necessarily a bad thing; whole-leaf hops are great for dry-hopping, but pelletized hops are much easier to measure and give you greater control of your beer's bitterness and the other flavor/aroma notes mentioned above.
Of course, if you've got the space and are considering growing some hops, then by all means, do it! You can always brew a nice IPA with them, and if you end up using more than you intended to, just let the beer mellow a bit over time. There's nothing preventing you from growing some hops and buying hops for other beers as well. If I had the space, I'd certainly grow some myself, but I'd still buy pellets from my LHBS for many of my beers.
If you enjoy gardening and have a good climate for hops, it is definitely worth it. There is something extra special about having a homebrew made with homehops.
That said, you will probably not have enough to supply yourself throughout the year, unless you have a much bigger yard than I do. My general habit is to make a wet hop beer once a year around harvest time (late August/early September for me) using the fresh hops right off the vine for late/finishing hops. I'll use store bought for bittering. If I have enough, I'll dry and use remaining hops for later batches.
There is satisfaction, and frustration, in growing hops. I personally have 6 hop varieties growing.
Unknown: Economics. Is it cheaper to grow your own? That depends. How much watering will you have to do? How much does water cost you? How much is your time worth? They don't require meticulous care, just watering and occasional checking for pests, and some early pruning work at the beginning of the season.