Whatever size they come in, I find that the best logos add to the company name. They don't just sit beside it or distract, they're seamlessly blended together whereby the whole is equal to the sum of its parts.
If you plan on designing a logo for yourself, Logofaves.com has a wonderful gallery of some of the best logos around. They even categorize it into Highest Rated and Most Favorited, and give you the option to Pin It onto your pinterest board.
Here are some of my favorite examples:
These are all fantastic, amazing and hilarious. They worked with what they were given to make something clever and awesome, and they make me want to buy their products, whatever these products may be. (Elephant combs?)
Their tag line is "The Heart of the Community", so we decided together to incorporate the heart into the logo design. It'll be displayed on the signage in 2013, so look out for my baby if you're ever in hankering for a gay old time in Winnipeg!