www.example.com/widgets.htm

1. Many directories (and other potential linkers) will not link to a subdomain.

2. even if people link to www.example.com/, rather than deeplink to widgets.htm, that page will still get some benefit.

3. If you later expand:
www.example.com/widgets.htm
www.example.com/red-widgets.htm
www.example.com/green-widgets.htm

you still have just one domain, so all incoming links will benefit every page indirectly, plus you have only one site to promote, and visitors have one site to navigate.

Whereas the other way:

widgets.example.com
red-widgets.example.com
green-widgets.example.com

These are all separte sites, any incoming links you do obtain will divided between three domains.

4. www.widgets.example.com is the ugliest URL in the known universe; generally speaking, if you have a subdomain, lose the WWW - widgets.example.com.

For true domains, keep it - www.example.com - (But the choice is yours!).

Seconded: www.widgets.com/directory

What if each subdomain would be a seperate niche? IE Gaming, Health, etc. Would it be best to have each niche have niche.mydomain.com/pages.html or have mydomain.com/niche/pages.html?

I would define niche by audience; ie if the topics were different but related, with - broadly - one audience, I'd stick with folders and one domain.

If the target audiences were different, then the advantage of one domain shrinks, and there's a case for separate domains.

But even so, I'd go for new, independent domains, rather than subdomains, in most cases.

Having said all that, I think it has to be a case-by-case decision.