I think they do.. Thesis is one such theme hugely popular for its SEO properties

absolutely YES, but you must modify from standard to SEO based. It is very easy, just use SEO plugin available on the internet.

In optimization, themes does not play a considerable role. But for user's standpoint themes play a major role.

A good theme with good site structure and navigation brings back visitors to your website.

For on-page SEO, yes definitely, especially how your header tags are implemented.

They do well because they have all of the required/suggested document elements and formats.
Using one of the SEO plugins and well formatted permalinks helps with individualizing everything. Also, some themes are better than others at their on-site seo.
WP is also good for easily inner-linking your pages, which is a benefit.

[DELETED]

Well.... a WordPress theme that is already SEO optimized does the job well in getting traffic from search engines because they are coded correctly and complies with all sorts of rules exist for theme coders to follow. This helps you to get the organic traffic you needed thus maximizing your earnings at the same time. With an SEO optimized theme you have an edge against other bloggers out there.

I will agree that the best WordPress SEO theme is the Thesis Theme.

Yes Themes Play their role for Search Engine Optimization!! You have to select the theme which have less page loading time and more customizable options!!

[DELETED]

[DELETED]

How a Theme is designed is very important. SEO plugins are only one half of the picture. The Theme does matter.

A key thing to remember is to make the job of indexing your site as easy as possible for a search bot. HTML is structured in a very specific way to allow the hierarchy of information on your site to be easily figured out by the likes of Mr Google et al.

If you stick with creating your site using HTML how its supposed to be used then you will be well on your way to giving Mr Google what he wants without making him work too hard. A well designed theme will take these things into consideration.

For example (as a very simple example) your theme should have a sensible arrangement of H1,H2,H3 tags etc. Usually your theme will at least take care of the H1 and H2 tags for your home page, pages, post etc, associating them with you Site Title, Tagline, Page or Post titles (depending on the theme settings)

Often themes with good extra seo features will let you do extra things too like change the Read More links into something more useful to make it even easier for Mr Google to figure out what your site is about.

SEO plugins are great for taking care of things like meta information, rewriting HTML titles, no-indexing pages etc, but you need a solid SEO base in your theme to start with.

The Theme is the foundation.
The SEO plugin is the icing.
And your content is the tasty jam and cream bit in the middle

..and now I'm feeling hungry.

Of course, there are small optimisations like the use of header tags and having alternative text in your images, but the effect of those is debatable, but Some themes undo the search engine friendliness built into Wordpress through poor construction.Wordpress have the ping command,it is good for seo

[DELETED]

Yes, I see some difference with wp themes. If I use CTR theme not fully support home page meta contents. But default WP theme supports well