I had two 19" CRTs for many years and they didn't look that bad. Then I replaced one with a 20" LCD and suddenly saw how horrible the other CRT looked. So I replaced that with a 24" LCD, and now the 20" looks a bit small. I still use 1024x768 on one laptop and 1400x1050 on another though, so I haven't completely forgotten how it is to work on screens with lower res. And like the previous poster said, if you're mainly doing wordprocessing and some occasional image editing then a 19" will work fine.
However, if you use a lot of windows and/or photoshop or equivalent software then you'll be happier with a higher res screen. 20" with 1600x1200 is the minimum I'd reccommend for more "advanced" use.