What changes do narrow-body airliners undergo to serve (relatively) long routes?
The 737 ER (Extended Range) differs from the rest of its family by having an extra fuel tank extending its effective range.

Legally speaking (for US registered aircraft) you don't need to carry life preservers for each passenger, if you are only flying over land routes. So if a plane is being used for say a JFK $\rightarrow$ Nashville route, they would not be required to carry life preservers; but if they decided to use the plane on an over water route, they would have to outfit it as such. 

Inter-Country travel may also effect the outfitting of a plane, as various countries have different equipment requirements (although most are the same now). Long haul routes may very well translate to non domestic routes, which means the plane may need to be outfitted with extra equipment that is capable of working on foreign systems. 

There may be some paperwork involved around certifications as well. For example the FCC does not require domestically operated aircraft (commercial and GA) to have radio station licenses; however, it's often required by many foreign entities. A domestic only plane may need to obtain one of these licenses before heading to is destination.     

On a bit of a side note the pilot must also be familiar with the destinations' regulations and methods of operation. For example here is a nice briefing from the FAA on flying into China.