margin: 0 auto;
<div class="col-lg-4 col-lg-offset-4">
<input type="text" class="form-control" />
<button class="btn btn-default" type="button">Go!</button>
</div><!-- /input-group -->
</div><!-- /.col-lg-4 -->
</div><!-- /.row -->
+1 The best solution, which the boostrap provides for solving the question's propose.
@static I have updated my answer, I removed text-center because it wasn't serving any purpose since the only content here is a block element, I also added a better explanation of the offset approach and provided a new centering method that supports any column size.
@static This was posted during the Release Candidate period of Bootstrap 3 and then there were no size distinction for offsets, so the fiddle was working with col-offset-4, I don't know why in my answer I did write col-lg-offset-4 though, I remember there were some discrepancies between the documentation and the actual Bootstrap files back then, so it's possible I mixed them up.
Note that this technique only works for even column sizes (.col-X-2, .col-X-4, col-X-6, etc...), if you want to support any size you can use margin: 0 auto; but you need to remove the float from the element too, I recommend a custom CSS class like the following:
You can use offsets to make a column appear centered, just use an offset equal to half of the remaining size of the row, in your case I would suggest using col-lg-4 with col-lg-offset-4, that's (12-4)/2.
actually your solution based only on col-lg-4 col-lg-offset-4 (also please fix the col-lg-offset-4). So in your solution you need to calculate manually the offset based on the col--size. If it was calculated wrong the text-center will not help to center the element, so it is useless here as I played with this in the jsfiddle. waiting for feedback.