You beat me to making this thread, oh-well, I'll ad some stuff to it.
First off, there is more then one Slenderman game, I recommend these as well.
Slender's Woods: It is either called that or something similar, but it is an attempt to make a sort of Slender game with more of a story of a guy who wanted to escape his life troubles in the old house he lived in as a kid. This house is deep in the woods as you would probably expect, and one of your last objectives is very surprising.
Haunt (The Real Slender Game): This is actually very well done for a free game. For what it is the graphics are incredible and the atmosphere is even better, with dense fog. Unlike the typical games, Slenderman will move regardless of whether or not you are looking at him, and the amount of notes you collect depend on the difficulty. There is something of a plot to this one too, sort of, the notes tell a story of someone who I presume you are looking for (have not played too much of it yet). There are also extras like photos of the person who entered before you and the like (though this person does not appear to be your average joe, at least if his shadow, letters, and what he leaves behind are anything to go by). Last is that your flash light will require batteries on any difficulty that is above "noob" (you also won't find any extras there either).
As for Slenderman traits, there are still more that are not mentioned, such as:
-Causing paranoia, insomnia, and pantiphobia (in some cases), and memory loss in victims.
-Is said to have some telekinetic and pyrokinetic abilities.
-Can created "Hallowed Ones", also referred to as "Maskys", which are people who are presumeably under the control of Slenderman to an extent, they also wear masks and have no memories of their actions when they "return to normal".
-Mind Control, to varying extents, similar to the last points, though some people theorize that he can't completely dominate you immediately, the more he is around you, the stronger his ability to influence/control your becomes. Minor things are as simple as influencing decisions to erasing memories, more drastic things are like what was mentioned in the previous point.
-Cameras will have poor picture display and/or audio quality on playback if Slenderman is nearby while it is turned on.
-In some interpretations, Slenderman does have a face, though you can only see it if you become more insane, and that staring at him too long will cause insanity. This goes with a theory that what you think Slenderman looks like is not what he really looks like, but rather the closest thing your mind can come to when it observe him, hence the insanity part when your stare at him too long.
-He can also make a location "supernatural" through some unknown process. It can cause a variety of eldritch things to happen, the most notable feature is that it will appear to be night time in this location regardless of the time and weather conditions around it.
Also, is anyone else into Marble Hornets here? Entry #65 recently came out, if anyone did see it...