Depends on the resolution more than the screen size and on how far away you sit from the screen. If the screen doesn't have at least 720 horizontal lines, you won't be able to play content at HD resolution. Note that it should still play, but will only be at standard definition resolution, the same as DVD. That isn't to say you will see no benefit at all - the higher bitrate and more efficient codecs of HD-DVD / Blu-Ray content may mean that the picture quality, colour depth etc. is better than standard DVD, but to really appreciate HD, you need a screen with suitable resolution.
Note also that smaller, older screens are less likely to have HDCP compliant HDMI ports, which may in future be necessary to enjoy HD content. At present,
AFAIK, no HD-DVD or BR discs have the image constraint token enabled, which prevents high definition output over non-encrypted interfaces, but that may change.
The other point is that you need to sit closer to a small screen to see the benefit of HD than you do to a large screen. You need to be about 2-3 screen widths (that's width, not diagonal) from your TV to get the most out of an HD picture. Beyond that distance, your eye simply cannot resolve the extra detail. The normal human eye can resolve detail down to approximately one arc-minute (1/60 degree). A 1080p picture has 1920 elements per row (1920x1080) and a 720p picture has 1280 (1280x720). So to see all the detail in a 1080p picture it needs to fill roughly 30 degrees of your horizontal field of view, while a 720p picture has to fill roughly 20 degrees.
A 26" diagonal 16:9 screen has a width of approximately 22.7". It is highly unlikely that your 26" TV has a 1080 line resolution, but the calculation below holds for any screen size. Some 24" computer monitors have a resolution of 1920x1200 and are capable of 1080p, so this might apply to them.
Let ideal viewing distance v be determined as a function of screen width w and angle a.
Simple trigonometry gives v = w / 2tan (a/2). For 1080p this gives v = w / 2tan 15d = approx 1.9 screen widths, while 720p gives v = w / 2tan 10d = approx 2.8 screen widths. For a 26" screen this equates to viewing distances of around 42 and 64 inches for 1080p and 720p respectively.
Hope this helps.