The screen on the eee PC is pretty damned impressive. The tiny screen on my old 3-Com Audrey was just about the same physical size as my 4G Surf, but it packed in about half the pixels. These days you get an easy 800 pixels across in such tight space that my old eyes simply can't count the dots.
Of course, you are still taxed with a 'short' display. It's not a problem in Terminal or in your web browser, because you can scroll. But sometimes you get a window that's too big and you can't get to the close or okay buttons. The fix for that by the way, is to hold Alt while clicking and dragging the window around.
Looking for more space in Firefox? - Open up Firefox. Right-click the toolbar somewhere such as over-top the Stop button. If you don't use the Bookmarks bar (I never do) you should uncheck that. Also notice how big the buttons are in Firefox? You can downsize them. Right-click the toolbar again and choose 'Customize'. In the window that pops up, look to the bottom for an option to 'Use Small icons' and check that box. You have just increased your browsing real estate. You may even decide to part with your status bar (but I like mine too much). To remove it, click View and uncheck Status Bar.
Want more space in your taskbar? - Taskbars are always over-crowded but the eee PC has a little less horizontal space than you may be used to. How about getting rid of the word 'Applications' on the Application button? An eeeuser.com forum poster, Red Penguin found this remarkably easy method. Simply right-click the Applications button, and click Properties. Now just uncheck the option 'Show title in button'.
Another space eater is the Desktop Switcher. It looks like four big boxes in the right hand corner. This is handy if you spread your windows across separate spaces (one desktop for work, and one for games?). I have never really made good use of this feature and you don't need the switcher panel to switch desktops anyway (you can press Ctrl+Alt+Arrow Key and get the same effect. To get rid of the desktop switcher panel (it's actually called the "Pager") right-cick it and Remove it.
I am still collecting space saving tips myself - so I my add to this topic in the future. In the meantime here is what my tight-on-space desktop looks like.