No, it's not really possible, because if it could it wouldn't be dark.
To see why this is, think about some some collection of gravitating particles which is going to to collapse to a smaller, denser collection of particles. To do this they need to lose a lot of energy: you can see why this is by thinking about where the average particle lives in the gravitational potential of all the particles.
Ordinary matter – clouds of gas and dust say – do this by getting extremely hot as they collapse, and then radiating energy electromagnetically. Ultimately collapsing clouds of gas can get hot and dense enough that nuclear fusion can start and we get stars.
Dark matter, by hypothesis, doesn't interact electromagnetically, at all: if it did it would not be dark! This means that the only way it has of losing energy is to put it into the average kinetic energy of the particles, and that means that collapse doesn't happen, because if you have a lot of particles with lots of kinetic energy they don't stay collapsed. The virial theorem is important to understanding this.
So dark matter simply lacks a mechanism to lose energy since it can't radiate it away electromagnetically, and so does not collapse.
(In fact I think there are some mechanisms: dark matter could lose energy by gravitational radiation for instance, but this is an absurdly slow process except in really extreme cases.)
To answer the second part: it certainly was (perhaps is) a possibility that there are very large numbers of compact, massive dark objects which make up dark matter. These things are known as massive compact halo objects: MACHOs (the alternative theory is weakly interacting massive particles which are, of course, WIMPs, and there are I believe also RAMBOs although I'm not sure what they are. If there are not ARNIEs there should be (perhaps one kind of these will be CONANs?)). These might either be failed stars, isolated planets or (I like this idea) small black holes: there's a wide range of possible BH masses below stellar mass BHs and the point at which they start becoming bright due to Hawking radiation. In the case of small BHs these would probably need to be primordial (made in the big bang) as there's no plausible mechanism for them being the end-point of stellar evolution.
But it turns out that such objects are observable. Because they are massive they will deflect light, and they can therefore be detected by gravitational lensing as they pass in front of more distant luminous objects (stars, really). Well, you can do the statistics of how many of these things there would need to be (which is really a lot), and how often you would expect to observe lensing events from them as a result. And then you can do a survey and look for lensing events. And the results of such surveys (some of these are pointed to by the above Wikipedia article) are that there are not nearly enough MACHOs to account for dark matter, although I think there is still a little wiggle-room, depending on who you ask.
