Technically, you can use a table anytime for any reason you want.
However, if you want to build an up -to-date web site with Web Compliant Web Pages following the latest Web Standards, than I highly recommend that you follow the guidelines (steps) explained on this web site.
Also, for a complete list of web standards, see http://www.webstandards.org/about/mission/.
What about making a photo gallery? Nope, no tables. This can be done quite easily using CSS and div tags, or even an unordered list.
What about making a form? Again, the answer is no, tables are not necessary when making forms. Use the label control and float it to the left, make it a block box, and give it a width. This will help you line up the labels and input boxes.
. Form example: label {float:left; display: block; width: 120px; text-align: right; margin-right:4px;}
If you do it for purely selfish reasons, than do it for the traffic you can generate to your site. Huh? What's that mean?
I mean, Web Sites that are web compliant will generally achieve better SEO scores and generate more traffic than non-compliant web sites.
The Search Engines, such as Google, have become very sophisticated. I have no doubt that things like Compliancy and Accessibility play a role in SEO now, and will play a larger role in the future.