Because Piccolo knows he would lose very badly to Vegeta. He is also interested in improving himself to himself, not to try and get strong enough to beat somebody he will never beat. read more
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Closest they ever got to getting in a scrap was when Vegeta bumped into him on the Lookout and kept on walking and Piccolo looked back at him and gave him that "n*gga, hell nah" look. There was a time (non-cannon) when Piccolo grabs Vegeta's head because he turned into jello at the sight of this guy. read more
On Dragon Ball - General, a GameFAQs message board topic titled "Ok seriously why hasn't vegeta vs piccolo happened yet". read more