This is a really really hard question. I'm a sucker for horror type scary moments. Things that jump out at the player usually scare me. So the wall masters in oot and mm were pretty startling for me. Also I played a Myst like called Lighthouse as a kid and the game has very few animated characters in true Myst like fashion. But at the very end of the game as you explore the main villain's lair if you make a small mistake and forget to turn off the monitoring systems you'll eventually turn around and you will be treated to a video of the boss just a few feet away from you with a pipe in the process of clubbing you for what will likely go down as the most scared I've been by a video game. This was particularly startling because there is absolutely no warning. Its not like this is a horror game. There is barely anything that moves at all in the game. You are just wandering around for hours and hours quietly pressing switches and solving puzzles and then randomly there is a creepy looking guy RIGHT BEHIND YOU with a pipe.
It helps that I was but a tiny child at the time.
But am I really intimidated by these things? I was totally surprised by my pipe wilding friend in Lighthouse.
You must be aware of the danger.Speeches don't really do it for me. Generally I associate eloquent speeches with nerdieness which is hardly an intimidating trait. When enemies start pontificating I start to think they are all talk. This is particularly true in a game where my character's powers come from actions.
Words aren't intimidating by themselves.Big enemies aren't inherently intimidating either. I thought Shadow of the Collosus was great, but those bosses seemed quite week despite their size. When I saw them I was kind of in awe of how cool and big they were but I didn't feel a second's hesitation to run right up to them, climb up their bodies and stab them in the head. In fact it was so easy, and the aesthetics were so dark I started to feel bad about it and just looked up the ending. I was glad I didn't finish it, I wouldn't have been satisfied by the game. Still think its pretty great though.
Size doesn't matter.Then there are the comic book guys. The Gannons, the Bowsers. I've never been intimidated by these guys even as the tiniest child. Beyond the fact that they sometimes make speeches, which makes me subconsciously label them as a nerd, the challenge they present are exciting more than anything. They have unique abilities. Defeating them is important to the plot. Also, players know the implicit truth that these bad guys must be defeatable.
Your story's big bad is almost never intimidating. I left the almost b/c I may have missed something and it seems counter intuitive but I have yet to think of a time the main bad guy, the one that is hyped, the one who is diametrically opposed to the hero truly intimidates the main player. They are the point of the game! They exist as a counter point to the hero's strengths and weaknesses. Beating this person gives the whole experience purpose. Why would I shy away from challenging him, her, or it? I always look forward to these encounters. I may get a nerdy speech! In fact, the bigger and more powerful you make this person the more fun, exciting, and interesting facing them becomes. As a designer you want the player to be thinking "bring it on" in this situation anyway.
Someone brought up invincibility.
They must be beatable. This is a game. If the enemy cannot be avoided or defeated people will stop playing. If you are facing an enemy IRL who is unbeatable I feel bad for you b/c quitting is not an option, but in a game it is and players will quickly figure this out! If the idea is that the player is supposed to stay alive for a certain period of time they will likely feel abused, angry at the enemy, and possibly angry at the game, but they will not be intimidated! As soon as the player gets the potion of vulnerability he or she will likely immediately seek out the enemy for retribution. This is not an intimidated person.
They must seem dangerous. I'm not really an art guy, and I know there are some hacky designers who rely totally on aesthetics to try to get their points across but it would be equally hacky to completely dismiss them. Give them ragged clothes, make them look strong, give them claws, have them be asymmetrical, blah blah blah. You could start a thread in art about designing an intimidating character and I would have little to contribute but I'd enjoy reading it. The key point here is if they don't look the part, people will just think its funny. Think of the rabbit in Monty Python. Oh yes, don't forget music and sound effects!
They must BE dangerous. Here's the real kicker and where true game design shines. If an enemy looks scary but is very weak or harmless within the game's ruleset eventually players will learn this and not be intimidated at all. Give them lots of hit points and powerful attacks. Make them move quickly. Give them special abilities that are hard to counter.
I think a really nicely done intimidating enemy is the Big Daddy from Bioshock:
This one scene demonstrates all my things.
TLDR: just read bold then watch video
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