Is a 1080p resolution television worth the extra money?

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This is incorrect, or at least incomplete.

It depends on the size of your television and how far away you are sitting from the tv. If you are sitting far away from a 55" screen, you may not be able to tell 1080 from 720 or even standard definition. On the other hand if you sit very close to a smaller tv, you may be able to see the difference between 1080 and 720. Your eyesight also plays a part - it all depends.

As far as I'm aware of, all over the air HD broadcasts are 1080i. However, while some consider 1080i to be inferior to 1080p, both can produce the same 1920 x 1080 resolution picture. The difference is 1080 is interlaced, like 480i and 576i standard definition. The reason 1080i video tends to be inferior is that most broadcasters reduce the bitrate to try craming more channels per channel/transponder, where as Blu-ray discs which use 1080p don't have this bandwidth issue and thus use a much higher bitrate than over the air broadcasts. Like standard definition channels, some HD channels may be just 1280 or 1440 pixels across. For example, BBC HD is 1440 x 1088 pixels interlaced.

Blu-ray discs and other HD sources (e.g. Full HD downloads) typically use 1080p. The advantage here is that the TV does not need to deinterlace the picture, eliminating any risk of interlacing artifacts showing. However, a drawback with progressive video is that 24p motion will typically appear more jumpy, where as with an interlaced source motion can occur at each field, effectively doubling the refresh rate.

To overcome the issue with progressive video such as 24p, most high end TVs use motion compensation to interpolate in-between frames. This is why you'll see TVs claiming high refresh rates like 100Hz or even as high as 200Hz. So besides 1080p, another thing worth checking is the TV's refresh rate. If it doesn't mention, then it likely does not have motion compensation.

In my opinion, unless you use a Blu-ray source or are lucky enough to have HD broadcasts that use high bitrates, the difference between playback on a 720p display and a 1080p display is not going to be great, regardless of the size of the TV. For example, a low bitrate 1080i broadcast is going to look poor (maybe not even HD-like) no matter how good the TV.

Some are 1080i and some are 720p.
The European Broadcasting Union recommends 720p/50Hz.

The only Free-to-Air High Definition channel in Denmark (DR HD) is 720p/50Hz.

I can notice a difference on a 46" screen sitting 10' to 12' away between 720p and 1080p. My wife can't or more accurately, does care enough to notice.

I think its silly to take a 1080 signal and downgrade it to 720, I can see the difference too, depends on the TV as well.

Another thing that effects what you see on an HDTV is the sharpness of your eye sight. If you have poor eye sight or your glasses/contact lens prescription is out of date then you may not notice a difference between 1080 and 720 resolutions. The prescription for my contact lenses are newer than for the glasses I wear and I can see much more detail when I have the contacts in my eyes. With the glasses I can't see nearly the difference between 1080 and 720 but it is still there. IMO, the reason many people that can't see the difference might be due to the quality of their eye sight.

I've seen very little, if any, difference between 720p and 1080i/p on an 82" DLP set...
I'd be more than surprised of someone could tell the difference in a double blind test...

The main real-world advantage of 1080p is not the extra sharpness you'll be seeing, but instead, the smaller, more densely packed pixels. In other words, you can sit closer to a 1080p television and not notice any pixel structure, such as stair-stepping along diagonal lines, or the screen-door effect (where you can actually see the space between the pixels). This advantage applies regardless of the quality of the source.

And what source are you using?

TV signals (in Oz) look like they've printed an SD picture out, photocopied it a few times, faxed it for good measure, then stretched it to fit a HD resolution

Nasty!

Watching an upscaled DVD on 720p or 1080p, I can tell a difference between the pictures on my 46", but not on my 32". My missus couldn't tell the difference between SD & HD channels on either TV, but the difference is like night and day.

Dish HD at 1080i/p (varies), Toshiba HD DVD A3 and Panasonic Blu Ray player...
Due to our location we don't get broadcast HD but are limited to 480i digital broadcasts which look much better than analog SD broadcasts...
And The Boss could care less about the picture quality...

Sucks @ the 480i.
Everything in Oz is 1080i, which has been f.u.b.a.r, except for one smart mob which broadcast in 720p, but usually just show low quality SD handycam footage, or crap quality international (non-english) news anyway

GO S.B.S!
I really mean that ... i just wish SBS would go away