The only way to do this with Bootstrap "out-of-the-box" would be to use 4 columns and stack the items in each. This isn't ideal for dynamic content when you don't know how many items you'll have in each column. Also the items order top-to-bottom, and not left-to-right.
<div class="container-fluid">
<div class="row">
<div class="col-md-3">
<!--item1-->
<!--item2-->
<!--item3-->
<!--item4-->
</div>
<div class="col-md-3">
<!--item5-->
<!--item6-->
<!--item7-->
<!--item8-->
</div>
<div class="col-md-3">
<!--item-->
<!--item-->
<!--item-->
</div>
<div class="col-md-3">
<!--item-->
<!--item-->
<!--item-->
<!--item-->
<!--item-->
</div>
</div>
</div>
Otherwise, you have to use a jQuery plugin like
Masonry or
Isotope, or using CSS3 multi-columns.
Jquery plugin method
Bootstrap Masonry Demo
Bootstrap Masonry Demo 2
CSS3 columns method (Masonry-like CSS solution)..
This is not native to Bootstrap 3, but another approach using CSS multi-columns. One downside to this approach is the column order is top-to-bottom instead of left-to-right.
CSS3 multi-columns Demo
There is also more detailed info in this answer to a similar question.
Update 2018
Bootstrap 4 includes a Masonry-like solution using CSS3 multi-columns:
Masonry cards Demo
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