Yay shoes!! 
I tell you, it really depends on the person, but here I go:
My favorite tennis/running shoes are Mizuno's. They great lines for all types. I have a neutral foot so I don't need support on the inside, however, my husband does and so we found him some with moderate support. SO, i love that they have shoes with support. Second, They have a wave plate that allows for the shock absorbtion in the heel to move throughout the length of the plate (usually 1/2 or full length of shoe). My second favorite brand is Saucony. I have literally have had about 5 pairs of these. They feel like I am walking on pillows. I have not had much experience with their non-neutral shoes. I have not fallen in love with Asics, but they do have good shoes. Be aware of their Middle of the line vs. top of the line. Make sure that you are getting what you need out of your shoe.
My favorite comfy, casual shoes are Merrells. They are the number one repeat buying brand in America. I really think that the comfort I get with these is worth the price. Also, they have a large selection of styles and colors and are designed for a woman's foot. Oh, and they are easy to wear right out of the box.
My dress shoe (for slacks mostly) are Dansko or Ecco. These are expensive, but I am nearly positive that Danskos are approved by the APA (American Podiatric Association). When I worked at the mall, I could wear my Danskos for nearly 11 hours and my feet didn't hurt a bit. Also, they are the stapled clogs that most nurses wear for 12 hours on end. Very good shoes. I like the Eccos because they aren't as bulky. They have a sole that molds to your foot over time and is VERY durable. The bottoms are made of bouncy ball material and have shock absorbtion. I was also able to wear these shoes right out of the box...The Dankos take some getting used to with their rocking motion. It helps to eliminate all of the work that your calves and feet do and lets the shoe do the work.
For sandals, Choca's are good and have good arch support. Merrell also has really comfy sandals. I haven't tried, but really want to, Moszkito sandals. They look to have very good arch support for flip flops. Honestly, I am partial to my Adidas Soccer sandals. They have a great footbed, similar to that of a Birkinstock. http://www.birkenstockusa.com/foothealth
I know that some of these are expensive, but they last forever. Especially if you take care of them. I spray ALL of my shoes with a silicone waterproofer. Make sure it can be used on leather and mesh. A can is usually 5-10 bucks, but it really does make the shoes last.
OH, I almost forgot...the danskos, eccos, and birkenstocks are european brands. They don't measure in wides because of how they make their shoes. They emphasis the holding of the heel in the heel cup and allow your toes lots of wiggle room. My husband has wide feet and was able to buy the European equvalent in Eccos (3 different pairs) and hasn't had any trouble. Also, because they use high quality leathers and materials, they mold/stretch to your foot.
Let me know if you have any questions or comments. Hopefully this helps. I know that if I am walking for a day (doing shopping, going to the park, tourist-ing) I make sure I am wearing some of these shoes and not my overly cute ones.
Hope you have a fabulous Friday!!
Aimee