To position the content of the column div you can use the responsive versions of justify-content-* class with d-flex

<div class="row">
    <div class="col-md-4 d-flex justify-content-md-end justify-content-center">
      Email
    </div>
</div>

Just add the classes d-flex to display flex and justify-content-md-end to align at the end of the column for display md and upwards and justify-content-center to align to center for display xs and upwards.

Demo

Bootstrap 5 (update 2021)

Since flexbox is still used the centering methods in Bootstrap 5 work the same way. Columns can be centered using offset, auto-margins or justify-content-center (flexbox).

Demo of the Bootstrap 5 Centering Methods

Bootstrap 4 (original answer)

There are multiple horizontal centering methods in Bootstrap 4...

• text-center for center display:inline elements
• offset-* or mx-auto can be used to center column (col-*)
• or, justify-content-center on the row to center columns (col-*)
• mx-auto for centering display:block elements inside d-flex

mx-auto (auto x-axis margins) will center display:block or display:flex elements that have a defined width, (%, vw, px, etc..). Flexbox is used by default on grid columns, so there are also various flexbox centering methods.

Demo of the Bootstrap 4 Centering Methods

In your case, use mx-auto to center the col-3 and text-center to center it's content..

<div class="row">
    <div class="col-3 mx-auto">
        <div class="text-center">
            center
        </div>
    </div>
</div>

https://codeply.com/go/GRUfnxl3Ol

or, using justify-content-center on flexbox elements (.row):

<div class="container">
    <div class="row justify-content-center">
        <div class="col-3 text-center">
            center
        </div>
    </div>
</div>

Also see:
Vertical Align Center in Bootstrap

I'm not sure if you want horizontal or vertical center. The simplest way to horizontal center is to use mx-auto (auto-margins) on the inner w-75 divs...

https://www.codeply.com/go/orlziQBanZ

<div class="container">
        <div class="row align-items-center">
            <div class="col">
                <div class="w-75 mx-auto" style="background-color: grey;">
                    <form>
                        <h3>Sign In</h3>
                        <label class="sr-only" for="email">Email</label>
                        <div class="input-group mb-2 mr-sm-2">
                            <input type="email" class="form-control" id="email" placeholder="Email">
                        </div>
                        <div class="input-group mb-2 mr-sm-2">
                            <input type="email" class="form-control" id="password" placeholder="Password">
                        </div>
                        <button type="submit" class="btn btn-primary mb-2">Sign In</button>
                    </form>
                </div>
            </div>
            <div class="col-1 mx-auto">
                <h2 class="text-center">OR</h2>
            </div>
            <div class="col">
                <div class="w-75 mx-auto" style="background-color: grey;">
                    <form>
                        <h3>Sign Up</h3>
                        <label class="sr-only" for="email">Email</label>
                        <div class="input-group mb-2 mr-sm-2">
                            <input type="email" class="form-control" id="email" placeholder="Email">
                        </div>
                        <div class="input-group mb-2 mr-sm-2">
                            <input type="email" class="form-control" id="password" placeholder="Password">
                        </div>
                        <button type="submit" class="btn btn-primary mb-2">Sign Up</button>
                    </form>
                </div>
            </div>
        </div>
    </div>

The align-items-center on the row is for vertical centering.

Use:

<!-- unsupported by HTML5 -->
<div class="col-xs-1" align="center">

instead of

<div class="col-xs-1 center-block">

You can also use bootstrap 3 css:

<!-- recommended method -->
<div class="col-xs-1 text-center">

Bootstrap 4 now has flex classes that will center the content:

<div class="d-flex justify-content-center">
   <div>some content</div>
</div>

Note that by default it will be x-axis unless flex-direction is column