My website is getting fairly large now and in order to make it grow I am considering purchasing some well established sites and then I intend to put the sites that I purchase on a subdomain of my main website.
Is this a good or bad idea?
Also if the site that I purchase is getting lots of traffic and I redirect traffic from the original domain name to my subdomain, can I get in trouble with the search engines?
Interesting approach, and one I have never really thought about. It could be an excellent way of expanding your site's area of service and expertise, but I'd say there are also a lot of factors that you need to be cautious about.
For instance, I can see this working very well in a case such as the one Nikolas mentioned above, where you integrate sites with smaller ones that provide services that are natural for your main site to feature. That way you can get some good exposure, and open up for more return traffic as the visitors of the merged site discovers your main site. You should be careful though, because not all sites are "natural" to merge, and that means that if your main site doesn't provide anything that the visitors of the "disappearing" site will appreciate, I think you might as well let it live on its own.
Another point is the status of the site you plan to close down and merge into your main site. If that site has a strong community, its followers are most likely to be upset that the foundation of their community disappears, even if you have a nice community for the main site.