I just upgraded today (from iPhone 4) and my plan did not change. The only difference is my unlimited plan got dropped, and I was switched tot he 2 GB plan automatically. My minutes, text and features otherwise did not change. I even kept my TEC service. The salesman didn't even ask if I wanted to switch plans, they just transfered it over 🙂
Nothing in your plan should change if you upgrade, unless you have unlimited data (doesn't matter what phone you have or what phone you upgrade to). As of the end of June, if you upgrade by signing a new two-year contract and get a subsidized phone, you will lose your unlimited data and move to a tiered data plan, as LinkRS indicates (there's also A LOT of threads about this on this forum); again, it doesn't matter what phone you have and what phone you upgrade to. You also could choose to move your entire account to the Share Everything Plan.
To maintain your unlimited data, you'll need to pay full retail price for the phone, get the phone from someplace like ebay, or use another upgrade that may be available on your plan (also lots of threads about this on this forum if you want to do a search).
And if you haven't heard yet, as of this spring, there's also a $30 upgrade fee (lots of threads about this, too).