@deereinhardt this one is highly regarded and is safe to use with lots of features

http://wordpress.org/extend/plugins/nextgen-gallery/

@deereinhardt I agree with Paul about NextGen being a great tool. Another possibility is to use tools and badges from picture sites like flickr (http://www.flickr.com/help/blogging/) – provided, of course, that you host some of your pictures there. Their badge is built quite simple, but works great on WP (http://www.flickr.com/badge.gne)

@amyhallbiz, with the Wordpress Gallery, is there a way to get both the image title & description (that you can set for each image) to show?

I have to 2nd @deereinhardt – I’m looking for a professional, really nice gallery. NextGen is nice, but not high end (at least without doing extreme customizations)

I love nextgen, but it does require some customization. It is so fast and easy to upload and sort in bulk. One problem is the pagination. If you have a lot of images in a gallery, and you select paginate, then it refreshes the entire screen and you need to scroll back to the bottom to see the next page of images. This totally drives me nuts! 
I love prettyphoto lightbox, but it is so slow! I think highslide is the best lightbox for speed, versatility with captions, though not the most flashy.
I do like the idea of using either Flickr or Picasa (especially with the new G+ integration) for SEO visibility. But it does require an external call which can slow the site. Shashin is the best Picasa plugin, but Mike Toppa has just had to revamp it and it is very buggy right now and causes many other jquery plugins to break. This has a lot to do with the G+ / picasa integration. (I think this was a bad choice for Google to force this, but that is another blog) 
So Flicker plugins are the best way to get the both the incomparable visibility and SEO and great looking galleries. But as a Google evangelist and hugely anti Yahoo, I am ashamed to have concluded this comment with that statement.