I am trying to turn off the page title display on my whole site, as I don't want the title of the page on all the pages.

I'm using the twenty twelve theme.

Is it possible to do w/out upgrading to custom CSS?

Thanks!

Am I right in saying that this option...
... is for custom menus and won't work in pages?

No, it's for pages, but it requires a custom menu, so yes you are confused!
The regular top menu automatically displays labels that link to all your published pages, and the labels are the actual titles of the pages: if you edit the pages and delete the titles, they will vanish from the menu as well. Replacing the regular menu with a custom one allows you to display labels that aren't identical to the actual titles of the pages: this includes label on the menu but no title on the page, if you apply the trick I"m explaining in the post timethief linked to.

Am I right in saying that this option...

Tabs for pages but no page titles on the actual pages:
After you add the pages to the menu, click their arrows to open them, type an additional character in the Navigation Label, click Save Menu.
Go to Pages > All Pages, hover under each page name, click Quick Edit, replace title with   (HTML for a space), click Update.
Back to Appearance > Menus: delete the additional character from the Navigation Labels, click Save Menu.

... is for custom menus and won't work in pages? Though I may well be severely confused/deluded about what I just said. In which case is the Custom/CSS option the only route for my needs?

Agh, I love sounding like a total newb :-/

I create say a 'Contact' page, and it's all fine except that it displays a large bold 'Contact' word at the top of the posting. The fact that it's highlighted in the menu is sufficient for me and this additional version is just taking up space!

Any thoughts welcome, I've had a search but not finding what I need.

Thanks in advance, Sidx

The tab in the top nav menu doesn’t have to be the actual page title, so here’s what you can do:

Edit the pages and delete their titles.
Go to Appearance>Menus and create a custom menu. Select your (now nameless) pages from the Pages module, click Add to Menu. Click the arrow at the right side of each page module to open it, type the title in the Navigation Label field. Click Save Menu, select the menu from the Theme Locations pulldown, click Save. http://en.forums.wordpress.com/topic/duster-theme-double-headers?replies=5#post-616357

I don't think purchasing a premium theme would make any difference. This is a new bug that's probably due to the recent WP updates, it was reported by another user as well who was using a different theme, and it has to do with the deleting of the titles (which you're not really supposed to do).

I inserted the code as per your instructions and it worked perfectly! Thank you, thank you, thank you...

timethief... I totally agree with you about white spaces and simplicity, hence why I chose the Twenty eleven template.

There is a major glitch happening with the site this morning. On the Laurie page, a new title appears "Previous Post". I've gone ahead and re-created a custom menu... But the problem appeared again! How do I fix this?

A million thanks to you both for your help. This is my first time using WP forums and I'm blown away!

P.S. On a personal note I'm visually challenged and I wish more bloggers had more "whitespace" on their blogs for ease of reading. I also wish more used smaller images. These days it's apparently assumed that we are all viewing blogs on monitors the size of drive-in movie screens, despite what the stats indicate. :)