Shulchan Aruch C.M. 409:3 says:
אסור לגדל כלב רע אא"כ הוא אסור בשלשלאות של ברזל וקשור בהם ובעיר הסמוכה לספר מותר לגדלו וקושרו ביום ומתירו בלילה
It is forbidden to raise harmful dogs unless he chains them with iron chains. In a border town it is permitted to raise them and chain them by day and let them loose at night.
The Biurei HaGra explains this is limited to Israel, but the Ramo goes on to include the limitation outside if the dogs are potentially harmful to people. The purpose of putting them in chains (in the latter case) includes preventing them from scaring pregnant women (מאירת עינים there), so the chaining has to be obvious, not just effective.
The analogy to gun control seems fairly obvious. Permitted for self defense, even in ways which have some theoretical possibility of harm (at night in a border town), but otherwise precautions must be taken to prevent accidental harm to others. There was, however, no decree to outright ban them.
In addition, in terms of sales (analogous to background check requirements, I guess) Avoda Zarah 15b says it is forbidden to sell, make or fix weapons for someone (Jewish or not) who one is concerned will use it for murder.
In terms of "inalienable rights" Judaism doesn't have (to my knowledge) any Halachic or Hashkafic approach which worries about Government encroachment and tyranny. However, one of the rights recently recognized in the second amendment is self defense (the recent DC vs. Heller decision), and this is recognized in Judaism not as a right but as an obligation, about oneself as well as in defense of others. (Sanhedrin 72a and 73a respectively).
Some of these same sources and additional ones are discussed in this article by Rabbi Shlomo Yaffe and he uses them to apply some thoughts to gun control, including the Ramban on Bereishis 4:20 which discusses the "guns (swords) don't kill people, people kill people" slogans you hear every once in a while.