AinOhdMilvado — There are actually not so many “zechuyot” for an oleh chadash today. (I am someone who did make Aliyah with Nefesh B’Nefesh, so I know from whence I speak). Basically it boils down to some cash (called the “sal klita”) over the first 7 months that you live here, very small amount of money towards rental assistance for the first few years if you don’t buy a house, free health insurance for the first year (after which you have to pay for mandatory insurance like any other Israeli), 75% tax instead of 125% if you buy a car within the first 3 years, the right to bring in 3 lifts of household items tax free, and possible help towards college degrees if you are young enough. Oh, and the State of Israel will pay for your one way airfare to come, and give you a free ride from the airport to anywhere in the country.
On the flip side, I can perfectly understand someone wanting to keep their foreign citizenship. We are still in Galus, of course, and people feel it is prudent hishtadlus to keep their options open. (The U.S. has no problem with dual citizenship, so that was not an issue for us — but I make a point of keeping both our Israeli and U.S. passports current for the same reason.) Additionally since Israel is a country with a mandatory draft for all citizens, there are people who are nervous about becoming citizens and having to send their kids to the army. You may feel that is not right, but it is definitely a real factor to many people, particularly considering the dismal situation for frum people in the IDF.
As far as the original question — there are many legal ways to move to Israel without declaring Aliyah and becoming a citizen — the most common ones are via a student visa or the “permanent resident” status described by The Chassidishe Gatesheader in his very informative post. However I believe that yungerman1 is wrong about the kids. My understanding is that although the parents are not citizens, any children born in the country have the automatic status of citizens unless the parents specifically renounce it. If you don’t want your kids born here to be citizens, make sure to renounce it formally after each birth.