Is a Nikon d90 worth buying when I already have a d40?

I currently have a Nikon d40 with 3 lenses: 18-55mm, 28-70mm, and a 70-300mm. Recently someone suggested that I should get a d90, as they are apparently much better. Is this true? Also, will the lenses I currently have work with the d90? (the lens diameter of the d40 is 52mm) Mainly I want to ask if the d90 is worth paying the extra several hundred pounds for, when I already have a perfectly good D-SLR.
As a subtext, I would also like to ask about filters. Do they make a difference? And how do you even attach them to the camera?

The D90 is a significant upgrade from the D40, although the D40 is still a viable camera.

Just for clarity, the filter diameter is 52 mm on the lenses you have, NOT the camera. You can use the same lenses on the D90 as well as many legacy AF lenses which would have to be manually focused when used on your D40.

The D90 also has a video mode if you should like to explore that aspect of the new dSLR.

If your images are this good from your D40, you might consider buying a nice used D90 at some point.

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Yes.

However, the D90 was replaced by the D7000, so you might want to look at that instead.

The D90 is probably one of the best DSLRs on the market. Here's a comparison to your camera:

The D90 has 12.3 MP while the D40 has 6.1MP. The D90 also has a 3.0" LCD compared to the 2.7" LCD on the D40. You can also use the LCD while shooting instead of having to always look through the viewfinder. The D90 also has a DX-format CMOS imaging sensor, which the D40 doesn't. Also, the D90 capture images to SD/SDHC memory cards, while the D40 only works with old-fashioned SD cards. The D90 also has HD video.

The Nikon D7000 has 16.2MP, a DX-format CMOS sensor, full 1080p HD movies with Full Time Autofocus, and a 3" LCD.

Filters are pretty much necessary for professional photographers. There are a few types of filters, but most people just buy a UV filter (protects the lens from dust/damage), a Polarizing Filter (saturates photos, eliminates glare and reflections), and a Neutral Density filter (darkens image for long exposures; graduated and fiters darken part of the image). Filter size is determined by the size of your lens. Most lenses are 52mm or 58mm. The lens size is usually found on the underside of the lens cap or on the bottom of the lens.