First off, who is the "they" that want little tiny robots inside everyone? That is most definitely science fiction.
Nanotechnology encompasses a whole range of technologies. Basically, it is defined as "any structure created at the nanometer range", which obviously is a pretty vague definition. Every time you use your computer you are using nanotechnology. Same with every time you wear sunscreen. Or whenever you buy a computer part that comes in one of those static-shielded bags.
A lot of people are worried that so-called "replicators" will be programmed badly and will basically convert the entire Earth into more replicators. However, there is no reason to think that would ever happen. This planet has been covered with self-replicating nanomachines for at least the last three billion years. Also, there is a very interesting
article written by Eric Drexler that you should look at. Basically it talks about how self-replicating machines would be a very inefficient way to do macro-scale contruction, and instead advocates a "nanofactory" in which things would be constructed first by nanomachines, then put together by larger and larger robots until a human-scale device/structure emerges (hence the term "exponential manufacturing".
As for the "nanobugs in your bloodstream" that you are worried about, would that really be so bad? A DNA-based "nanobot" has already been constructed that attacks cancer cells without hurting normal cells. It's quite interesting as well, you can read the news story
here.
Nanotech is cool.