Bootstrap Accordion - start all closed

Boostrap 3

Just remove .in from panel1.

<div id="panel1" class="panel-collapse collapse">
   <div class="panel-body">Contents panel 1</div>
</div>

Bootstrap 4

See @Syed Sajid's answer

For Bootstrap 5 you also need to collapse the button else while the body won't show, the heading will still be highlighted and the icon indicating the card is open will still display.

Default is;

<button class="accordion-button" type="button" data-bs-toggle="collapse" data-bs-target="#panelsStayOpen-collapseOne" aria-expanded="true" aria-controls="panelsStayOpen-collapseOne">
        Accordion Item #1
</button>

You need to add collapsed to the button & tell aria it's not expanded like this;

<button class="accordion-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#panelsStayOpen-collapseOne" aria-expanded="false" aria-controls="panelsStayOpen-collapseOne">
        Heading Text
</button>

Then the body can be dealt with as normal by removing show from class="accordion-collapse collapse show"

<div id="panelsStayOpen-collapseOne" class="accordion-collapse collapse" aria-labelledby="panelsStayOpen-headingOne">
 <div class="accordion-body">
  Body Text
 </div>
</div>

Bootstrap 5:

add class collapsed to accordion-button

<button class="accordion-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseOne" aria-expanded="false" aria-controls="collapseOne">
    Accordion Item
</button>

remove class show from accordion-collapse

<div id="collapseOne" class="accordion-collapse collapse" aria-labelledby="headingOne" data-bs-parent="#accordionExample">
    <div class="accordion-body">content...</div>
</div>

Bootstrap 4 and 4+ remove class show from collapse show

<div class="collapse">
    <div class="card-body"></div>
</div>