There's nothing particularly magical or special about 1080p. Unless you're specifically watching 1080p video, there's no specific reason to target 1080p any more than any other resolution.
That having been said, a higher resolution will always look better. A 20" 1680x1050 will look nice, a 24" 1920x1200 will look nicer, and a 30" 2560x1600 will look nicer still. There are other factors to consider too. Image quality varies widely between monitor types, with most cheap LCDs sold having TN panels (lowest quality), and the higher end models having VA and IPS panels (which look much nicer IMHO).