It is extremely important to know information about the root structure to avoid belowground competition when growing stuff in tight space. However, it seems that such information is very hard to be found on the Internet. Is there any online database, book or whatever other sources that contain comprehensive information about plant root (of common horticultural plants and crops)?
There isn't really a general resource regarding root spread - the best you can do is try to research root spread for each individual plant you want to grow if its really a concern to you. There's probably more on crops and their roots (a little bit here to show how variable it is http://www.cropsreview.com/plant-root-system.html) but with regard to other plants like shrubs, perennials, etc., grown for their aesthetic appearance, although you can assume the roots of a woody plant will have a much wider width and depth than those of a perennial, root spread is difficult to predict in open ground. When roots meet obstructions, or inhospitable conditions, they veer in another direction, so predicting quite how far away they've gone and how deep isn't easy.
In regard to planting, its usual to work out what distance you need between plants in terms of topgrowth, so height and spread of any plant you're growing is a critical piece of information when thinking about proximity to other plants. This is why information on, say, growing vegetables from seed, will give a measurement or recommended distance between rows and between seeds - its based on the spread of topgrowth as the crop grows. You would, when planting a hedge, plant much more closely than if you were growing a single specimen because you want to create a solid barrier, and its desirable to have the topgrowth of each plant mingling together; there are recommended distances for hedging plants too, again, based on topgrowth rather than root size.
So generally, that's what you think about when planting rather than root size, although root spread is an important consideration when planting in a restricted space such as pots or other containers: an obvious example of the importance in those circumstances is planting a climbing specimen which makes 35 feet in a shallow trough - though it might grow initially and make a foot or so, it will soon start to look rather unwell and stop growing.