Hindu Mythology also has many superstitions, some might have scientific reasoning behind them, many do not. (I know this because I am a Hindu myself.)
Some examples are :
Cutting nails after sunset
Cutting nails at night (or after sunset) is bad luck. A variation of this is that one isn't allowed to cut their nails on Saturday. I believe that in the olden days, when electric lights didn't exist, people used to cut their nails with scissors(?!) and cutting their nails in the dark would result in massive pools of blood all over the place because people wound up cutting their fingers off or something. I do not know about why Saturday is a restriction.
Taking clothes off the washing line at night
This is also supposed to be bad luck. The rationale behind this is that at night, the ghosts and demons are active. Some of them maybe hiding in your clothes, and when you take them back into the house, you are effectively inviting them into your homes and allowing them to wreak havoc.
Hanging a lemon and a chilli on your front door
This practice is supposed to ward off evil. A string is pushed through the lemon and chilli and is tied (only at one end) around a nail over the door. The resulting contraption of dangling chilli and lemon is supposed to keep evil spirits out of your house (I do not know how, my mom never was able to explain that one). They can still get in if you do things to invite them, like whistling at night for example. Which brings me to the next superstition...
Whistling at night
This brings demons into your house. No explanations there. Just really angry aunties shouting at you telling you not to invite the demons over for dinner.
Staring at shadows at night
Shadows at night you say! If there is some external light source, then you should be able to get shadows at night. Of course if you looked at these shadows, you have inadvertently invited demons to your home. When I was a kid it seemed like almost anything I could do would invite demons home. I think this superstition started because little kids could get nightmares looking at strange shadows before they slept at night. I know I did, after I heard about this superstition.
Returning to the house for any reason, just after you left it.
Not only is this bad luck, but be prepared to waste a lot of time, depending on what your parents choose to believe. Many people believe that if you leave the house, and immediately return (to pick up those car keys you forgot to take the first time around), you will either be KILLED on your journey, or have horrible luck until you return home. (Whew, at least demons don't get into your house this time huh?). To avert certain disaster, there are a few things you can do. Some people believe it is enough to get get back into the house, sit down for a minute and then walk out again. This would probably be enough to convince the demons who were out to destroy your car (or horse, or airplane) that you didn't really start on your journey the first time. (Hey I said they weren't getting into your house. I never said demons weren't involved here). Other people believe that when you get back in, you MUST drink a glass of water and THEN sit down. Still others believe that you should walk in and out of the house five times(thus confusing those pesky demons. Now they won't know whether you're coming or going). And finally there are a few people who believe a combination of all these methods is a good way to ward off the demons.
Leaving your hair open on a full moon night
I believe that this applies to girls (mostly). So you thought you were smart by hanging that lemon chilli contraption over your door eh? You forgot about your daughters/sisters/wives walking around with their long tresses flowing over their shoulders at night! The ever present demons will be seduced by their hair, and climb into the hair, and enter your houses that way! I believe THIS superstition came up because mothers did not want their daughters to attract extra attention from boys, and on a full moon night, there would be more visibility than on nights without a moon (Remember, we are talking about a time before street lights). I think I also have to mention that open hair is considered to attract boys/men in Indian culture (I feel that this is a given, but I still thought I should explain it)
Too much flattery
This is bad for the one who is receiving the praise. The idea behind this is that the demons will get jealous, and then decide to hurt you out of envy. So if someone keeps telling you how good you look, then you have to touch your temples with your knuckles to remove the "kaala nazar" (literally translated that means "black sight", but it basically means the 'evil eye')
Staring at the moon during Ganesh Chaturthi
I know this doesn't apply to everyone, but it has some interesting roots, so I wanted to add this in my list.
Ganesh Chaturti is a festival celebrating the birth of Lord Ganesh. On one of his birthdays, tripped and fell while he was dancing on his flying rat.. (yes. I said it. Flying rat. Or mouse if you would prefer. I'm really not making this up. Lord Ganesh himself was a boy whose head was chopped off and replaced with the head of an elephant. Try explaining Hindu mythology to little kids and see how many of them you can terrify.)
Anyhoo, when the moon saw this, he laughed at Lord Ganesh. Not a smart thing to do, laughing at a God on his birthday. So Lord Ganesh cursed the moon, saying that no one would ever look at the moon on his (Lord Ganesh's) birthday. So if you DID look at the moon, you would incur the Wrath of God.
There are many others, and I will add the interesting ones as and when I remember them, and if anyone knows any others, they can message me or add them here themselves.