Hii @bradfordshrimp. I figure you refer to third party widgets. 
Here primarily use Social Network widgets from Facebook, Twitter and Google+. Also use some social share plugins through my widgets. 
I use the Headway Theme which allows me to control my widgets in a great way. When I started out my blog ended up a little to cluttered with widgets. But now I am getting better control of it. 
Just like you I am working to simplifying my blog. Will move more towards a magazine style. I just love how you now can identify valuable touch points for your blog with Google Analytic. 
Cheers..
Are MorchHotel Blogger

@bradfordshimp  I agree with @eugenoprea.  The more widgets you have, the more time it takes your website to load.  I have a few social buttons in my sidebar, but nothing besides that. Even those I look at warily when my site has some lag time.  

@kristi-hines Yeah I noticed that it takes a bit longer to load websites with many widgets. Noticed you hardly used anyone. Interesting, I might have to look into take out some of my widgets. 

They dont slow my page to much. But don’t experience a lot of conversation either from widgets. The various Social Plugins I use seems to be more effective.

Cheers..
Are MorchHotel Blogger 

I like to look at widgets as part of the website design and content. You widget areas and sidebars should add to the content and complement the website design.

If you have a blog on Social Networking would you throw a random post on “My Favorite Family Recipes” in?  Probably not. Lots of folks look at widgets and sidebars as space that needs to be filled and fill them with irrelevant space fillers.

One way of using sidebars is to promote other content on your blog or site.  I like a simple yet powerful widget called “Mini-Loops” which allows you to selectively display information on other content.

Another indispensable plugin is one which allows you to build your mailing list to keep in contact with folks who visit your blog.  A sign up form is different from a members list.  You should offer a premium, a newsletter or some other reason for people to want to stay in contact with you.

Want some good examples of sidebar widgets?  Take a look at the ones on this page.  They are not filling space but adding value to the reader experience.

As for minimizing widgets they are integral to WordPress design.  Widgets may add some overhead and come at a minor cost in perfomance but they are good and necessary.  Don’t be afraid to use widgets when they add to your site’s value. 

@aremorch Just an unnecessarily large image file sizes. Using my photography site as an example, I could upload the photos in two ways.  I could upload the full resolution file image (4.7MB) and resize it on the blog to 900 x 640.  Or I could upload the photo at 900 x 640 (400KB).  

Screenshots typically aren’t so bad on filesize.  The ones made by Jing (free version) are usually optimized pretty well.  I made one in Jing and then did a screen capture of another image in the same size.  The one by Jing (.png) was 47KB and the one I print screened, pasted into Gimp, and saved as a .jpg was 136KB.  Quality-wise, they are the same.  Jing’s is actually a bit nicer because you can add arrows and text onto the screenshot at the same filesize.

While the difference between 47KB and 136KB doesn’t seem like much, you have to realize just how many images are loading on your blog.  The background, the icons, author bio pictures, gravatar pictures, etc.  So if you can shave off a little here and there, it can make a big difference in how quickly your site loads.

Now I realize why my favorite blogger is a pain to load. He’s a widget warrior for sure. I’ll have to pass this on to him. It would sure be nice to speed him up a bit. Thanks.