Why don't Jews try to convert other people to their religion, outside of Israel?
Since Christian and Islamic forces try to make them a minority shouldn't they also try to convert people to grow larger? Or is it just that Islam and Christianity originally came from Judaism so there is no need?
Jews have different expectations of non-Jews than other religions have of their non-faithful.
Jews believe that all people are commanded to obey G-d, and His commandments create a powerful and holy connection between Him and each individual. The commandments that apply to everybody are called the 7 Commandments of the Children of Noah.
There is another, higher level of connection to G-d embodied in [hundreds of] extra commandments which create a stronger and more personal connection to G-d. These are the commandments which apply to all Jews - the mitzvot. Once you are on this level these mitzvot apply to you and your children forever, even if you renounce or ignore them.
To understand how and why this second category arose you will have to do some historical research, but in the present day the point to remember is that Jews don't believe that someone on the first, basic level needs to take on the obligations of the second, higher level. It would be a beautiful, praiseworthy and commendable thing, but because of the more extensive obligations a potential convert is raising the stakes in a serious way. If they prove themselves inspired and dedicated to fulfilling the extra commandments then the Jewish courts will accept and welcome them as new Jews, but many conversion candidates have an sadly shallow understanding of what they are taking on. It is better for them to stay as non-Jews than become Jews who transgress and ignore G-d's will for them.
As a result, in general the Jews are happy for the rest of the world to remain as they are. We accept self-motivated converts after extensive study and practice, but we do not seek them out or proselytise. There are institutions and individuals who help non-Jews who want to learn and keep the commandments that apply to them, but as you can imagine the focus has always been on helping Jews learn and keep their own mitzvot.
As usual, there are many answers to this question, all of them are related.
First, let's start with a brief history. In the time of Abraham, Abraham did try to convert many people. He did this by having an open tent which allowed people from every direction to come and learn about Gd. Then, in the time of the Exodus from Egypt, the Jewish people again, accepted any converts who would come to the Jewish people and become part of the nation. In Jewish tradition these people were referred to as the "Eruv Rav" or the "Mixed multitudes of people" who did not come from the Israeli tribes, but who saw the miracles that happened in Egypt and wanted to attach themselves to Gd.
Traditionally, the Eruv Rav was the source of many bad things that the Jewish people did. Some explain, that this happened because while they were awed and inspired by Gd, they were not truly loyal to the Jewish people.
Jump forward a few hundred years, and before the time of Christianity, the leaders of the Jewish state, were fighting a war with the Idumeans. After winning the war, and being tired of the constant fighting over generations, the leaders decided to convince the Idumeans to all convert to Judaism. They did so, and centuries later, some Jews of Idumean decent (namely King Herod) attached themselves to Rome, became leaders of Israel and were very cruel to the Jewish people. Again, their loyalty to the Jewish people was questioned.
So Jews in general, do not like mass conversions of people who are joining the "winning team". There is a question of their loyalty to Judaism and the Jewish people. In other religions like Christianity and Islam, this is not such a big deal, because those are religions made up of many nations, while Judaism is a religion only made up of a single nation. You can't be Jewish and not be part of the Jewish People.
On another level, we are not concerned about losing many members, or not having enough Jews around. In the Torah, Gd says not to count the Jewish people directly, or else a plague will come about. We are also promised that we will be an eternal nation. We will never die out. Because of this promise, and a general statement that our numbers should not really be counted (except when absolutely needed, like to build community projects or help the poor) there is no concern that we are "too small", or that other groups of people are larger than us.
From the perspective of Judaism, we know what is correct and right for our people. We know the Truth, and we are not in competition with anybody else in the world. We share what we know about Gd and his unity, and about living in a Just society. The rest of the details of how other nations live is not our concern. As long as people act Justly and Peacefully and don't try to take away our home from us, we let other people live however they wish to live.
To expand on Yoel's answer: The Jewish people, collectively, are obligated to keep the 613 commandments in the Torah (the books of Genesis through Deuteronomy). Non-Jews, as Yoel notes, are only obligated (in our view) to observe seven basic commandments given to the sons of Noah. These include: A commandment to establish courts of justice and to not permit blasphemy, stealing, forbidden sexual relationships (e.g. incest), murder, idolatry, and eating flesh of living animals. Not too difficult, unless you like to eat "Rocky Mountain oysters" (if you have to ask, you don't) and certain shellfish that are eaten alive.
So when someone who wishes to convert comes to a rabbi, the rabbi will tell them that being a religious Jew is very difficult, very complicated, and very expensive (showing a conversion candidate a tuition bill for Jewish day schools should be a mandatory warning to every convert). Also, he will tell them how much hatred is even today still directed at Jews. He will say: "You are not doing yourself any favors by wanting to become Jewish. If you remain as you are and dedicated to the seven Noachide laws, you will definitely have a place in the World To Come. But if you convert, you will be obligated to observe the 613 commandments as they apply and you will receive Divine Punishment when you backslide." See Yevamos 47a.
However, if you have a conversion candidate who dismisses these warnings and says something to the effect of: "I hear what you're saying, Rabbi, but I am not content with just a share in the world to come; G-d has commanded the Jewish people to seek to be holy, because He is holy (Lev. 19:2), and I want that challenge, too," then you have a good convert.
There is no necessity for a non-Jew to become a Jew. Non-Jews also have an essential role in preparing this world for the world to come. They serve G-d through their own set of seven obligatory commandments which they must follow to ensure a place in the next world.
