My daughters are three years apart, and it's awesome. Starting when the youngest was about a year old, they played together very, very well. When the oldest turned 11, she started to outgrow "playing", and by the time she was 12 or 13, while they were friendly to each other, they were just at such different developmental ages, they weren't really friends who hung out. Now that they are 15 and 12, they are growing closer again, have similar interests, and have started doing things together again (independent of us). As in, my oldest daughter was going to ride her bike downtown to go shoe shopping, and completely unbidden she asked her sister if she wanted to go with her. That sort of thing.
My husband is younger than his brother by 3 years, and they were very close as young kids and again starting in high school (similar to what I'm seeing in my own children). He and his older brother lived together during college and grad school, and later in life, for about 10 years our families both lived in the same town and they were the best of friends. They probably saw or talked to each other almost every day and would hang out together when they both had free time. They moved across the country several months ago, and I see the hole that this has left in my husband's life. He misses him a lot, even though they talk on the phone at least once a week and facebook each other regularly. He's 40 years old and he misses his brother terribly!!!
So I'd say, yes, three years is fine. In my experience there is about a 3-4 year time period where developmentally they are just too far apart, but once the youngest hits middle school, they reconnect and continue to seek out and enjoy each others' company.