This thread is really interesting to me..in the past year or so, I've had several relatively new friends approach me with complaints about "my level of commitment to our friendship". Which has completely sent me running for the hills, in most cases, because I had no IDEA that they took our really (new, to me, at least) friendship so very seriously. To me, it was still in the "get to know you/form a connection" phase. A couple of semi-deep conversations doesn't mean I'm comfortable with being called 5 times a week or having them drop by my home unannounced or that I'd like to go underwear shopping together.

My closest friends are ones who can call if they have big stuff going on, hang out as life allows, and who can make a connection even if life has prevented us from talking for a couple of weeks. I'm *much* more emotionally intimate with these people, and tend to run from those who get disgruntled if I don't respond to a text with a link to an internet meme. I could just be a lousy girlfriend, though. I don't have these issues with guys.
Sudden death to a relationship, for me, comes when two people's lives are so enmeshed, time-wise, that they're staring at one another over half-empty bags of potato chips on the couch, bored, saying, "Whacha wanna do?" "I dunno. <sigh>" I can't abide friendships like that, mostly because I value my privacy.
Emotionally, the only reason I could imagine being "too close" is if the other person becomes so dependent on the other, that they lose their sense of autonomy in the world without the other person or start to lose their own identity/self respect/confidence. If someone needs to call me to figure out which shirt to wear to an outing, literally without being to make a decision for themselves without my official opinion, it's a sign that relational sickness has been reached (for me), and it's time to pull the plug. I try to keep a pulse on rather I'm keeping my own confidence, as well. Possessiveness is another huge deal-breaker. Life is too short for one person to hold another hostage, rather than letting them go be part of the world.
Other than that, I'm capable of forging connections with another person that really almost know no bounds, emotional intimacy-wise. They just have to be the right trustworthy individuals!