In order to be able to select multiple files in Sitecore's media file uploader, you need to modify the UploadMedia.xml file (located in sitecore\shell\Applications\Media\Upload Media). Specifically, you need to add the multiple="multiple" attribute to the input tag as shown below:

<input id="File" name="File" type="file" style="width:100%" multiple="multiple" />

Here's the full file:

<?xml version="1.0" encoding="utf-8" ?>
<control xmlns:def="Definition" xmlns="http://schemas.sitecore.net/Visual-Studio-Intellisense">
  <UploadMedia>
    <FormDialog Icon="Business/32x32/Paperclip.png" FormTarget="sitecoreattach" Enctype="multipart/form-data" Header="Upload File"
                Text="Select a file. When done click the Upload button." OKButton="Upload">

      <Script Key="Upload">

        function submit() {
        try {
        document.forms[0].submit();
        }
        catch(e) {
        scForm.invoke("ShowError");
        }
        }
      </Script>

      <CodeBeside Type="Sitecore.Shell.Applications.Media.UploadMedia.UploadMediaForm,Sitecore.Client"/>

      <input id="ItemUri" name="ItemUri" type="hidden" value=""/>

      <Border Padding="0px 0px 4px 0px">
        <Literal Text="File name:" />
      </Border>

      <input id="File" name="File" type="file" style="width:100%" multiple="multiple" />

    </FormDialog>
  </UploadMedia>
</control>

Result: