Actually I have meant in controlled airspace, but at an untowered airport (like most class E surface airports)
Ok, I've missed the class E bit. Please state to which country your question refers. In France, a clearance is not necessary for VFR flight in class E airspace (except night VFR), so if the weather is above VFR minima, you just take off and fly.
I was just wondering, if there are some regulations which forbids to take off at such an airport without SVFR clearance, when the automated weather reports weather below VFR but its clearly still VFR
If the weather is below VFR limits, but above SVFR limits (i.e., met vis on the ground >5km, in flight >1500m, cloud base >1500ft), then you cannot depart, land, or cross the airspace in question unless in reception of an SVFR clearance from the responsible unit.
In other words, if the weather is crap, yes you have to request an SVFR clearance--which btw, if you are on the ground it might very well be denied (generally in the interests of your own safety).
All the above is applicable to France, barring any mistakes I might have made. If you are talking about the States, it's bound to be completely different and you'll be better off asking a competent FAA instructor or posting in a US-oriented forum.