http://drupal.org/project/image
Current Drupal version compatibility: 5, 6
WYSIWYG Editor compatibility: Image module alone has no WYSIWYG integration

About Image module in general

Several modules can be "added on" to Image module to change or expand on its default functionality (discussed on later pages in this comparison) so these are the general details about Image module overall.

Image module has long been the most "common" way of using images in Drupal (not that it's perfect or ideal, but because it was first and it's all there was for a long time). Image module treats images as "nodes" that can be searched, commented on, etc, and it can automatically generate additional image sizes based on the original (such as thumbnail, preview, etc). Saving an image as a node can be beneficial, since nodes in Drupal are quite powerful and full-featured. On the other hand images as nodes can be "overkill" for some needs, such as when you want to just deal with images as standard "files" and nothing more (in which case IMCE module is most likely a better choice). Image module can be paired with a number of other modules to expand or alter its functionality, but it comes pre-packaged with a few things by default: "Image Attach" which lets you attach Image nodes onto other pages, "Image Gallery" for making a basic image/photo gallery, and "Image Import" for uploading images manually through FTP and converting them.

Benefits

• If Image module and its included sub-modules (Image Attach, Image Gallery, and Image Import) suit your needs, then there is nothing else to install, as everything is included.
• Image module comes with a basic "Image Gallery" sub-module. Nothing too fancy, but gives you a simple gallery, with categories, right out of the box. When you upload an image, you are able to include it in a category of your gallery, so that the image will appear automatically in the gallery.
• Image module has a mass-upload sub-module called "Image Import", which allows you to upload images into a specific directory on your server using FTP or other means, and then have Image Import turn those files into Image nodes all at once.
• Lightbox2 module works easily with Image module [add instructions]

Drawbacks

• The price of having everything "pre-made" and all inclusive in Image module is that it's substantially less flexible and cannot easily be changed. Image module is slowly being phased out, to be replaced by a similar (but much better, and fully flexible) solution based on more current Drupal technologies such as CCK, Imagefield, Imagecache, etc. There is expected to be an upgrade path, so feel free to use Image module for now if you need to.
• Though Image nodes get all of the basic benefits of being nodes, the Image Content type is set in stone, and cannot be expanded at all with CCK. You cannot add custom fields / field-types to expand the functionality of your Image nodes. If you add custom fields, they won't work.
• For adding images into other pages, the included Image Attach module is not likely to suit most people's needs since it: 1) only allows you to attach one image per page, 2) does not allow you to control where the image appears within content, 3) only allows you to float your image the right (default) or left of your content, and you cannot adjust it on a per-page basis (to change it to left instead of right, see the tip below).
• Image module uses its own method for creating scaled derivative versions of images (versus the popular and versatile Imagecache module), and is limited in what it can do and how many derivative image versions it can produce.
• Image Attach generates harmless but somewhat confusing messages after uploading an image.

Tips and Tricks

• By default, Image module places all new images on the front page of your site. Unless this is what you want, you should disable this first of all before uploading any images. Go to Administer > Content management > Content types (admin/content/types), and click on the "Edit" link next to Image. Expand the "Workflow settings" fieldset and uncheck Promoted to front page. If you want you can also disable Attachments and Comments on images here if you don't prefer those features.
• Enable "Image Attach" functionality on any Content Type you want to use it on ahead of time. Go to Administer > Content management > Content types (admin/content/types), and click on the "Edit" link next to the type you want to edit. Expand the "Image Attach settings" fieldset and change the Attach Images option to Enabled. Adjust any other settings you'd like as well and press "Save content type". Now when you make a node of that Content Type, you will see a "Attached Images" fieldset available, where you can upload an image or select an already-uploaded image from a list.
• Since Image Attach sets images to the right of the page by default, the way to change this to the left is to add the following into your own CSS file (you can only have one or the other):
  
  .image-attach-teaser, .image-attach-body {
  float: left;
  margin-left: 0;
  margin-right: 1em;
}

Screenshots

Image Attach: upload or attach one image to the page you're writing

Image Attach: image added to a page

Image Gallery: top view

Image Gallery: showing one category