The answer is “sometimes”. An address really helps to add credibility to your business, and to make it look more established. It can help create trust too because it makes your business look more open and not like you’re hiding your location from customers.
But, there is the security/privacy issue of your address being your home. I’ve not used my home as my business address because it makes me uncomfortable. And, when clients occasionally discover this (by trying to drop off a package, for example), most of them understand.
If that makes you uncomfortable, then you can consider getting a mailbox service. I don’t recommend a PO Box because it looks too purposely anonymous – and it’s obvious that you’re getting your mail at a mailbox. But, the UPS Store has mailboxes, and with those you get an official street address with suite number – which looks more official.
I’ve also seen people who don’t get a ton of urgent mail combine forces with an associate who already has an office and use their address as their mailing address.