This question is difficult to answer as it is not completely clear what you mean by 'steal'.

If somebody publically (on MO or another medium) presents an idea, problem or result it can happen that other people pick up the idea or problem and develop it further, solve it, use it and so on. Of course, when they do so they should, or rather have to, give appropriate credit to people contributing prior ideas/work, typically via mentioning/citing this prior work.

For example, here http://tea.mathoverflow.net/discussion/7/cite-mathoverflow/ is a discussion how to cite MO contributions.
(Perhaps there are other discussions of this form, this is the one I found.)

Using prior work, without giving proper credit, in particular pretending it is one's own work, is universally considered as highly inappropriate (a commonly used word in this context is plagiarism, copyright rather refers to something else). Plagiarism in mathematics happens, but it is rare.

So, depending on what you mean by 'steal' the answer differs:

If you do not want at all that somebody ever uses your ideas (not even in an appropriate way, giving credit) or works on a problem you propose, then what is the point of making them public? [This is addmittedly somewhat of an oversimplification.]

If you are only worried about inapproriate use of your ideas, then it is in fact a good idea to publically document that these ideas are yours , as if it shoud ever happen that they are used without giving credit, then you could point to this public record to establish your priority.
(However, cf. below, MO is rather not the right place for doing so.)

Having said all this, the main purpose of MO is (for all I know) not dissemination of new ideas or suggestion of open problems, but it is about asking and answering specific questions of which the person asking them actually suspects that they are *not open problems* and thus there is a reasonable hope that somebody else might be able to provide an answer (quickly/relatively easily).

Exactly as safe as it is to post such things anywhere on the internet where anyone who likes can read them.

I would like to see a site like MO to became a big scale cooperation that would have its own babies born ,be an example of how internet gives the benefit of many minds thinking together. Maybe at the future the research will be accelerated by large scale research sites. An idea of one ,the knowledge from another,etc. but how it will be true if none will site his idea because he want's hisself to be the one (or the member of the team) that solve something. I want to see site theorems at the future, how it could be done? the question might some day be :me or the science? are we working for our self-promotion or for mathematics.Because if we are working for mathematics why do we care if something would be under our name?If we have to choose will it be easy? since this day hasn't yet came i am wondering how many of you will post their trully research ideas in a site like this? if not what is the reason not to...

@minasteris: this forum is for question related to MO not general discussions. Thus, I will not continue the discussion after this post, but still provide a short answer.

First, some people actually try to carry out massively colaborative research projects in mathematics; however, facilitating such colaborations is not really the goal of MO. (This does not mean it is not a worthy goal, but the scope of MO is limited.)
If you are interested to read more about the projects I mentioned above you could start here http://polymathprojects.org/

Second, it was you who started to ask whether it was possible that ideas would be stolen. To which I answered basically that it is unlikely, but theoretically possible. Perhaps I did not stress enough that it is in my opinion very unlikely.
On a personal note, I openly discuss my research ideas with many people that are interested in them; of course, I do not post them on MO, yet not because I am worried that somebody might 'steal' them, but for the simple reason that it would be off-topic.

@an_mo_user: sorry but how i can propose a problem to the site that you linked?

i am ok with that but i just want an answer for the other link if possible

Allow me to direct users to Integrity Under Attack: The State of Scholarly Publishing, that appeared in Siam News from Douglas N. Arnold.
It suggests that plagiarism in mathematics is more widespread than one would naively think. Though I don't think MO would be a prime target
for the behavior suggested in that column, they went about it much more openly.

http://ima.umn.edu/~arnold/siam-columns/integrity-under-attack.pdf