Depends on what kind of airspace we're talking about. Is this Class B or C airspace? General info to follow:
First of all, know that ATC generally has NO idea whether you've filed a VFR flight plan or not. VFR flight plans are for Search and Rescue purposes only, stay at the FSS, and ATC will only get involved if FSS calls us looking for you because you're overdue. This is completely different from IFR flight plans.
Around Class C airspace, you're required to talk to ATC if you're in the C airspace, generally within 10 miles and below 4000' AGL. It's good practice though to talk to approach control if you're within 20 miles, and/or crossing the extended centerlines for the runways. Our finals sometimes get strung out 25 miles or so. I'd encourage you to get comfortable talking to ATC any time it's appropriate.
If you're operating around Class B airspace, you need a specific clearance from Approach to enter that airspace. You can sometimes operate underneath it without calling, but I still call whenever the freq allows me to get a word in. Again, the more you work with ATC, the more comfortable you'll become.