YAS. As I'm writing this, I'm going through a phase where I'm shooting almost everything blurry (a little bit of an exaggeration, but I'm pretty freaking obsessed with slow shutters right now). I love the life and imperfection that shooting at a slower shutter speed can add into the frame. It can make an energetic moment seem more energetic, it can make a quite moment seem more whimsical, and it can make a happy frame look giddy. It's a pretty universal mood-adder. Aside from all of that, I'm a big believer that perfection isn't everything. Inf act, it's not really worth much. A perfectly exposed image isn't really worth shit if it doesn't have any soul. Shooting with a slow shutter speed is one my my little internal nods to that idea.
Okay, so... what's considered a slow shutter? One of life's most meaningful questions. I typically shoot this type of work between 1/50th and 1/13th depending on how much blur I'm looking for. This is completely personal though so make sure you test out different speeds to see what works best for you
WHAT'S BLURRY, WHAT'S SHARP?
This is up to you. Shooting at a slow shutter can mean that the entire image is blurred or that everything is crisp with just one little bit of blur in a dress or in the hair. If you want the entire image blurry, easy. Shoot hand held and don't be afraid to move the camera as you're clicking the shutter. If you're only after a tiny section of blur, you can either shoot hand held or with a tripod (I never use a tripod) and try to keep everything still in the frame aside from that one thing you want to see blur in. Use a fan to blow the hair around, ask your bride to twirl in her dress, etc.
Keep in mind, shooting with a slow shutter doesn't mean that you're shooting a brighter exposed image. You still want to expose properly so make sure you bring down the ISO or use a smaller aperture if needed.