I've heard that the main electrical panel needs a GFCI outlet right next to it, and it also needs a switch to an overhead light. But I can't find anything on the net to confirm.
What you heard is an overextended composite of multiple, overlapping NEC requirements, so let's break them down in turn, starting with the receptacle. Its presence is covered by NEC 210.64 and Exception 1 thereto:
210.64 Electrical Service Areas. At least one 125-volt, single-phase, 15- or 20-ampere-rated receptacle outlet shall be installed in an accessible location within 7.5 m (25 ft) of the indoor electrical service equipment. The required receptacle outlet shall be located within the same room or area as the service equipment.
Exception No. 1: The receptacle outlet shall not be required to be installed in one- and two-family dwellings.
As a result of this exception, this is not something us DIYers necessarily have to worry about; however, it's a good idea to provision one anyway. If you are providing one, either by Code (in commercial/multifamily) or by choice (in single-family residential), the fact it is the panel service receptacle does not require it to be a GFCI. However, many panels are mounted in spaces (on the outside of buildings, in unfinished basements, in garages) where this receptacle would be required to be a GFCI by one of the 210.8 GFCI requirements, just like any other receptacle located in that space.
Finally, we get to the lighting outlet, which is a similar story to the GFCI. Panels located in well-lit spaces or outside do not need a light beside them, as ambient or room lighting is assumed to be sufficient by Code for service work, and temporary worklights, flashlights, or headlamps can be used if the space is de-energized. However, panels in unfinished spaces such as utility rooms and basements count as "equipment requiring servicing" for 210.70(C), triggering the lighting outlet requirement located there:
(C) All Occupancies. For attics and underfloor spaces, utility rooms, and basements, at least one lighting outlet containing a switch or controlled by a wall switch shall be installed where these spaces are used for storage or contain equipment requiring servicing. At least one point of control shall be at the usual point of entry to these spaces. The lighting outlet shall be provided at or near the equipment requiring servicing.
As a result, this may force the installation of a lighting outlet near the panel if none was provisioned otherwise; this is often a problem in homes that "scatter" utility equipment across unfinished spaces.
There's nothing in the NEC that demands a power outlet or switched light be installed by the panel. Indeed, some outdoor installations would make that impractical.
The caveat here is that a panel might be located somewhere that needs a GFCI outlet because of the location, not the presence of the panel. For instance, if your panel is in your basement (sometimes considered a wet zone), and you need an outlet in that room, it might be most economical to put an outlet like that next to the panel. Local codes might demand a light for the room as well.
It's not required but it's a best practice. I see a fair number of panels in commercial locations and even unimproved areas of homes that have a receptacle just inches away from the panel, a simple handy-box connected by a few inches of conduit. I assume this is an "electrician's receptacle" to allow him to plug in extension cords and lights so he can work on the rest of the facility. It typically goes to a dedicated breaker on the bottom right. The wires are long enough he could attach it to any breaker or even the hot side of the main breaker, naughty naughty!
I thought this might be a shibboleth of the electricians who work in this area, but I've also seen it in photos on the Web.
I haven't seen any that were GFCI, but I have made one GFCI because I needed to upgrade another circuit to GFCI. So I simply landed the other circuit on its 'load' terminals. Effectively you get a GFCI breaker for $16 instead of $45.