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I am absolutely amazed by various of ways to create a photo album in Drupal

Popular modules include:
Gallery: uses external gallery2 package
Acidfree: uses Taxonomy, Image, Video, and Views modules
related discussion can be found here
Also see gallery review at http://drupalmodules.com/module/gallery

Gallerix is another gallery module under active development.
It builds per-user album out-of-the-box. For each user, It creates a subfolder under files/gallerix/album/. Each image is NOT a node, which may be attractive for some people. However many features mentioned such as ajax commenting are available only with gallerix_widget_engine, which is not free. And I didn't see any batch uploading option beside using FTP.

brilliant_gallery also has quite some users.
It offers many features, particularly:
- Display and browsing through the images using slick Lightbox V2, or alternatively Thickbox, Greybox Redux.
However, only ftp upload is supported, and it doesn't provide per-user album. So it's good for single user photo site, but not ideal for a multi-user photo sharing website.

You can also use Flash gallery, which uses  SImpleViewer, a free, customizable Flash image viewing application. Or alternatively follow here instead of using the module. It looks very nice.

Angie Byron's article at lullabot.com "How to build Flickr in Drupal" uses the following modules:

• Image
• Image Exact Sizes (this module isn't strictly necessary, but it makes all the previews uniform which looks a bit nicer)
• Views (remember to enable both "views" and "views_ui" modules)

Flickr Gallery: a module inspired by Angie Byron's article

Besides using a gallery or image module, another popular approach is to use existing popular, almost must have modules, such as View, CCK, image_field, and image_cache.
For example, here is some discussion.
Actually there's a module doing this for you. Yes, it's true. It's called Yet Another Gallery Module, and documentation is available here

Another similar module of the type is: imagefield gallery
Here you can find detailed information on how to use this module

To summarize, there are several modules uses image module which create a node for each image
If using image field, then you can attach multiple values to one album/gallery node.
Depending on your application, a full node for image may be resource intensive, but does allow comments, rating etc. Also check out this article for more info on this, as well as here.

Any other approaches to build photo album?
And what is the best approach? (I know, I know, the question sounds very silly)

finally, here is the list of drupal photo gallery. It seems gallery module and image field+ imagecache are dominating the chart.