What do you consider a serious hill? See this thread for a variety of opinions:
http://forums.teamestrogen.com/showthread.php?t=31034
You can simplify all the tooth counts into just two ratios: Your lowest gear of 25:28 and your highest gear of 48:12. Divide them to get a single number like OnTerryOh explained. Whatever change makes the low gear result smaller will make it easier to get up hills. Whatever change makes the high gear result bigger will increase your top speed.
All the intermediate gears simply give you more options. They also let you pace another rider while pedaling at your preferred cadence.
A long time ago when I moved to [your old neighborhood], it only took one ride on my road bike to realize that I needed an MTB's lower gearing to get up the hills. This is despite riding almost entirely on pavement. That MTB probably had a 12-28 cassette and the same chain rings as your bike. It's low gear (probably 28:28) still wasn't quite low enough, but I suffered without complaint.
In 1994, my next MTB had a low gear of 24:28. That was a nice improvement, but I wanted still lower. I asked a bike shop for lower gearing but they said nothing lower was available. I now know there were such parts available! I would have paid them a king's ransom but I guess they didn't want the business.
I recently modified the '94 MTB. I now have a wonderfully low gear of 22:34.The price is that my top gear is now only 44:13, and my gear ratios are far apart (because that bike uses a 7 speed cassette). This means that "roadies" can fly past me, and I may have trouble pacing another rider.
So - do you need a bigger cassette? When you ride up hills, do you find yourself in the lowest gear and wishing you had an easier gear? If so, get a bigger cassette. Ignore what the experts say you should have. If the gearing isn't low enough, you'll be less motivated to go riding. And with less riding, you'll lose fitness which will make the gears feel even tougher.
Considering the general area where you live, consider changing to perhaps a 12-27 cassette. There is little reason not to - just the cost and the slightly wider spaced gears. The reason the bike came with a 12-25 is that in some places (like say San Jose) the lower gearing is just not needed.
EDIT: I looked up the specs for your Specialized Vita Sport: Sugino triple crankset 28/38/48. Shimano Nexave FD and long cage Sora RD. Shimano Sora 8 speed 12-25 cassette. KMC chain. Your rear derailleur is speced for a maximum cassette gear of 27. And with your crankset, it has 17 teeth of capacity left for the cassette range.
This makes it somewhat hard to install a bigger cassette because there are few 8 speed choices without going to an MTB cassette (which would require you to also change the rear derailleur). Shimano has a 13-26 cassette but that's hardly a change. You might gamble and push the RD's 27 tooth limit to fit a 11-28 cassette but you might not like the ratio jumps.




The price is that my top gear is now only 44:13, and my gear ratios are far apart (because that bike uses a 7 speed cassette). This means that "roadies" can fly past me, and I may have trouble pacing another rider.
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