Logos are something that you get to do, as a designer, as one of the first projects in design school. Usually it's your own logo, then a big group project for a restaurant (or something like that.) There, you will find if you really dig this thing called identity and branding in the design world, or if you want to run far away from being branded, yourself, as a “logo” designer.
I really enjoy designing logos and identities for others and have grown leaps and bounds as a logo designer since that first logo project 15+ years ago in design school. Logos are one of those projects where you get to study the person or the project that you are doing the logo for in great detail, you get to reseach what others doing the same service or similar service have as their own logo, and then you get to sketching and begin a creative process that takes time and nurturing. In the end, no matter how many rounds or ideas you've gone through with the client, you should arrive at something you, as the designer, are proud to show that you did and something that your client should display prominently and happily as their brand.
My most recent logo project was with one of my peers and mentor, Nathan Peel Photography. Nathan already had an identity with his first photography business, Fyrefly Photography. But Nathan dove into 2011 with a new business model, a new wedding business venture that targets new clientele and builds on his fantastic reputation that he's come to be known from with the Fyrefly business over the last few years.
The finished logo, shown below, with colors chosen for a social letterpress card that we'll be printing soon (shown second, below) and finally the Twitter avatar I created from both designs to re-inforce the brand in social media situations (shown third, below.)
As I mentioned above, the best part of the process of logos is “getting there”, below is a sampling of some of the rounds of logos we went through before arriving at the finished logo.
And I really enjoy seeing logos and identities working hard at welcoming new clients across the brand. I loved working with Nathan in custom tweaking a Wordpress template that we both thought would showcase his photography well for his new website. It is so so important for businesses to be brand consistent along all forms of marketing. Nathan's new business does this so well!

And lastly, here are a few more identities I've created that I think of as favorites.
There are a few more samples shown here on my website of previous logos that I've designed that I love. Logos can be created for new businesses, redone for existing businesses, or to just 'brand' an event, like the one you see in this link for Word Distribution’s trade show booth, where the theme for their booth was beach and the booth looked like a beach house.