It depends a lot on which beer you are making. If you are making a Belgian beer the yeast in most cases is a key flavour in the final beer, it would be a totally different beer without it.
If you are making an English or American ale, you can make them with any English/American ale yeast, but the result will be a bit different from the beer intended by the recipe. The yeast in the recipe is really just a suggestion. Part of the fun of brewing is finding out how different yeasts affect beer, and which ones you like best.
In and English or American ale you could use a dried yeast. US05 and S04 are both used by many home brewers, US05 is a very neutral yeast used a lot for American ales, but can equally be used for English ales. S04 is a more typical English yeast which produces esters, affecting flavour. Both these yeasts have liquid equivalents. Nottingham dried yeast is also widely used, and is available from Wilko as Gervin GV12. It is a pretty neutral English yeast, and there is also a liquid version of it. In my opinion, Nottingham and S04 are both decent dry yeasts, but there are much better liquid yeasts that will make an English ale significantly better. For American ales, I use US05, because it does the job well, IMO. And I use US05 in English ales in certain circumstances.
While brewers are learning the process of brewing it probably makes sense to use the dried yeasts. Many brewers carry on using them. Liquid yeasts cost more - but many brewers move on to them because there is a much wider range and you are likely to find a really nice yeast that really makes a difference to your beer. Brewers who use liquid often say they would never use dried again.
So you could make many of the recipes with a dried yeast, but you won't necessarily end up with making the beer as it was intended. It will still be good. Just different. When you are in the pub drinking one of those pints that make you go "Wow, that's amazing", the yeast and the management of fermentation is often a key factor in producing that quality. I think too many brewers focus on hops and grains, and miss out on the quality that yeasts can provide.