I was stopped for suspicion of DUI, not charged, but asked to appear in court. If I didn't go and it's been a year, was the case dropped?
No, your DUI case was not dropped. A warrant was very likely issued for your arrest for "failure to appear in court" (known as FTA). You haven't heard anything more because usually in these cases, the authorities merely wait until you are pulled over for an unrelated violation and then most likely bring you on charges for failure to appear; it's cheaper for the city than sending out officers to search for you. If you wait for them to stumble upon you, you will likely stay in jail until the case is resolved or have a high bail set on you.
A more favorable solution to your problem is to hire a lawyer to add the case to the court calendar and ask the judge to recall the warrant and then commence to defend on the charges. Because you are voluntarily appearing to face the charges, you have a good chance this will be allowed. This way, the judge is unlikely to even set a high bail and you may even be released on your own recognizance. You can even go to the criminal court clerk's office yourself and ask to add the case to the court calendar. In most places, they will not arrest you; however, you will still need a lawyer to defend you in court.
Failure to Appear in Court Because You Moved States
If the reason you did not appear in court for your DUI was that you relocated to another state, it does not mean your former state didn't issue a warrant for your arrest. Even though you are now living in another state, the state that you got the DUI in will still require that you take necessary steps as ordered by their state's court. In fact, if you are pulled over in another state, you'll likely be arrested and, perhaps, extradited to your former state.
The statute of limitations never runs out while you're across state lines. At some point, either voluntarily or by arrest, you'll likely have to "face the music," and by then, the ordeal may prove much more costly, both in terms of money and possible jail time, than it would have been originally. In addition, you may not be allowed out on bail because you have already shown yourself to be a "flight risk," which means you would be in jail while you await trial. Your sentence on the original crime of DUI or DWI will be enhanced because of the flight to avoid prosecution, as you've now committed two crimes.
Getting Legal Help
In this case, your best option is to contact, and retain, a DUI attorney in your former state, tell him or her your story from your new state, and have that attorney try to make a deal or "plea bargain" with the local District Attorney (DA) in your former state. The DA will likely be willing to recommend a less severe punishment for you, in exchange for your voluntary return to that state. The outcome is sure to be better taking this route rather than if you happened to be arrested and forced to come back to face the charges.