What are the regulations involved in aerial advertising? I often see small aircraft flying at a low altitude around beaches and the like with banner advertisements trailing behind them on a rope sort of structure. I have a few questions about them:


What sort of permissions does it require (FAA) ?  
Is this hazardous in any way (I believe there would be some
restrictions on this type of flight but is there an inherent danger
involved in such flights) ?
Are there any limits as to what altitude they are allowed to reach and
any restricted air space that they are only allowed to fly in ?
The short answer is that you need to get an FAA waiver (special permission), as required by 14 CFR 91.311:

§91.311   Towing: Other than under §91.309.
No pilot of a civil
aircraft may tow anything with that aircraft (other than under
§91.309) except in accordance with the terms of a certificate of
waiver issued by the Administrator.

(91.309 is about towing gliders, so banner towing comes under 91.311.)
You need at least a private pilot certificate to tow banners - sport and recreational pilots aren't allowed to do it - but since most banner towing is paid work, in practice the pilot will usually have a commercial certificate (this is from the waiver instructions):

When banner tow operations are conducted for compensation or hire, the
pilot must have at least a limited commercial pilot certificate
(without an instrument rating) and at least a valid second class
medical certificate. An instrument rating is not a requirement for
this operation.

The FAA has a complete guide on banner towing and the waiver issue process has more administrative details. There don't seem to be many specific airspace requirements apart from the obvious, e.g. no towing in a TFR zone. But the FAA can impose more or less any conditions that they like as part of a waiver, and it will include the approved times and areas for operation.
(As an aside, it's widely believed in the pilot community that the permanent stadium and Disney TFRs are really there to prevent banner towing, not to increase security.)