Should I Add a Blog to My Main Site or Put it on Another Domain?

SEO Question: Lets say I have a web service company (sales) site and a blog about proper web design at domain.com/proper-web-design/ Then lets say I have a blog about hot design sites at domain.com/hot-sites/

If the blogs becomes successful would it help domain.com in Google serp rankings?

SEO Answer: In a word, yes.

Quality links to any part of your site make it easier for the rest of your site to rank well. So long as you use good internal navigation your link popularity flows throughout your site.

Although you didn't ask the questions, as to weather your blogs should be 2 separate blogs or 1 blog and as to weather it would make sense to keep them both on your main site it really depends on what your goals are and how much effort you put into them.

If you market your main products or services too heavily on a blog it can become a bit harder for people to want to link at your blog. If your content quality is amazingly high you can probably get away with a good bit of marketing without it hurting your linkability too much, although I would recommend keeping the blog looking really pure and non commercial off the start in most cases to make it easier for people to want to like your site, subscribe to your feed, and link at your site. After a while you can flip the switch and make some bank :)

Also keep in mind that even if your main site did not rank better your blog may help establish you as a known expert in your field. Even without marketing your services on your blog some people will want to hire you based on what you write on it (I so am living proof of that concept). You also are more likely to get better leads from people you would work better with by taking leads from friends or working for people who like to read your blog than the lower quality leads search would provide you.

For higher end service based businesses I do not think search yields very high quality leads as compared to word of mouth marketing, building trust over time, and brand building activities.

Many people also do not realize how lucrative proper contextual ads can be in some verticals. In web design contextual ads may not be too great because most of your traffic is going to be people fairly savvy about the web. My mom is learning blogging and has a weight loss blog. She has been blogging for maybe 2 months now and already has got some organic links from other bloggers. Just yesterday, in spite of putting an affiliate ad in a post and three contextual ad units around it, my mom got a decent link from another blogger. Another friend of mine also recently got some great link love from a high traffic site with a rather plain looking blog because he had one of the few blogs in his vertical.