I have a business website where I have the marketing and support pages for a Mac app that I've developed. I also bought the domain name for the app which has the format myappname.com. Should I move my marketing and support pages to the app domain or keep them on the business website and redirect the myappname.com domain to my business website? I have seen other companies to it both ways. What are the implications for SEO, especially when I start to market my second app, which is completely unrelated to the first?
I think it's best to release all of your products under one domain name. One domain for one product usually signals to me: "This company is a one hit wonder." But when I see a product page that is part of a larger site that makes me thing "Hmm...I wonder what else they sell." I think it's easier to do cross-promotion when your customer intuitively understand that you have a family of products.
If you want to register myappdomain.com, go for it, but I would redirect it to subpage/domain on a larger site.
I think it only makes sense to have multiple domains/sites when deal with online services or some kind of portal (like Google and Gmail).
It depends. For the purpose of this answer, I'm going to assume that they are both .com domains, since Google’s algorithm favors .com/.net/.org TLDs over other TLDs (everything else being equal).
Two things you'll want to consider:
For example, let's say your business website domain is mikessoftware.com and your product domain name is mikesproduct.com. Searching in Google's keyword tool for [mikes software] and [mikes product] will likely yield extremely low numbers. In this case, everything else being equal, the choice of the primary domain name doesn't matter much (with respect to SEO, which was the issue of your question). In this example, I would likely stick to what I already have, in order to avoid spending unnecessary energy recreating my website.
On the other hand, let's say you sell appointment booking software, and let's assume your business website name is mikessoftware.com and your app domain is appointmentbookingapp.com. Searching for [appointment booking app] in Google's keyword tool and comparing the results to [mikes software] will likely yield much better results for [appointment booking app]. In this case, you may want to make appointmentbookingapp.com your primary marketing site to take advantage of the additional monthly searches. (Consider my second point below before making this decision.)
In this case, you can either redirect myappname.com to your business website, or use it to create a landing page for your app. Once you have your second product, you can create an other products page within your business website.
Regardless of which way you go, you'll want to retain ownership of both domain names.
Domain names are so inexpensive nowadays that you may as well keep myappname.com (and maybe even myappnameapp.com). They can be redirects to your main site or hold one site pages. Wouldn't you hate it if your competitors got those domains?
SEO aside, one approach can be to promote the products independent of the company. You can always link to the product sites from the company page and cross promote other products.
A good example is 37signals. They have product specific pages (basecamp, hirise, campfire, etc) have individual product FAQ / help pages but a centralized support ticket system running on the company site.
For a similar situation we use sub-domains, rather than domains. Make domain the generic probably the company name and replace www with each product.
And don't worry about SEO, trying to outsmart search engines isn't worth it, with the next Google engine optimization they'll break all your work.