What are things Brought down in Halacha that we do not do because of Danger?
Kitzur Shulchan Aruch 4:2 - Not urinating when one has the urge
Kitzur Shulchan Aruch 6:5 - Not pouring out water in homes next to where a person died
Kitzur Shulchan Aruch 32:17 - Drinking very cold water when tired
Kitzur Shulchan Aruch 33:
Kitzur Shulchan Aruch 161:20 - Cutting of Polish plaits
Kitzur Shulchan Aruch 177:
Kitzur Shulchan Aruch 199:13 - Leaving a freshly dug grave open overnight
1)There is of course Fish and Meat
2)Milk and Fish according to Sefardim and Minhag Chabad and some other Chassidim
3)Drinking water immediately after eating fish.SH"UT Rabbi Akiva Eiger says that the warning against drinking water shortly after eating fish is even today.It is also brought by the Kaf Ha'haim and the Aruch Ha'shulhan
1) Eating onions or garlic left overnight - there are ways around this, and some are not stringent about this nowadays
2) There are the various things mentioned in Tzavaas R' Yehudah Hachassid, such as not closing up a window or door, not having two brothers live in the same city, being careful about identical names when considering a shidduch, etc. etc.
3) Drinking water from a stream without checking for leeches
4) The practices mentioned in Yoreh Deah 116 - not putting money in one's mouth, not to eat sweat, and others.
5) The Sefer Shemiras HaGuf V'Hanefesh discusses just about everything on this topic.
What things are dangerous?
A.) Anything currently recognized by today's conventional medicine as dangerous.
B.) Anything codified into Halacha as dangerous.
The majority of medicinal statements in the Talmud were not codified into law by the Rambam or others. (In the 900s, the head of Babylon's yeshiva of Pumbedisa, R' Sherira Gaon, wrote: "the rabbis of the Talmud were not doctors, and wrote down the medicine of their day; do not attempt any Talmudic medicine unless our expert doctors today have established that it could do no harm.) The Rambam himself wrote in his medical advice as Halacha (parts of chapter 4 of Laws of Personality Traits), and again much of that did not make it into later sources of straight Halacha.
Something like "don't put coins in your mouth because diseased people may have handled them" appears Talmudically on down, and makes sense from our medical perspective today. "Don't eat fish and meat together" is the interesting exception, something that doesn't seem to be borne out by medicine today, but clearly made it into all the halachic sources (Shulchan Aruch etc.). The Magen Avraham (commenting on OC173:2) acknowledges this is the exception to the rule, and shrugs his shoulders at how it came to be halacha (though he accepts it as such).
Today, if you have a custom about these other safety things that appeared in non-canonical sources, by all means keep your custom, or talk to your rabbi if you feel you can't. Many such customs are described in the other answers here. Works such as the Hassidically-inclined Kitzur Shulchan Aruch have incorporated many such customs, and today we've seen a literary explosion of new books on these topics. If you have no such customs but feel it's right for you to adopt some of them, talk to your rabbi. If you have no such customs and don't want to adopt any, you're fine sticking with A. and B. above.
There are also things that are only "semi-dangerous" that should be avoided during the 9 days, like certain travel. I have a friend who broke up with a girl he was dating because she went sky-diving during the 9 days. I wonder what category that would have during the rest of the year...
Rabbi David Sedley has two pdf files on his website, where he brings the sources for different dangerous foods in Gemara and Halacha. Scroll down to the bottom of the page. These are from classes given at Midreshet Rachel v'Chaya.
Halachically Speaking Volume 3 Issue 9 (Avoiding Danger) also talks about many things that Torah considers dangerous.