When travelling most people prefer not to know what is going on back home and aren't to worried about the state of the Dow Jones, after all the whole point of travel is to get away from it all. However depending on where you are travelling and for how long then it might well be worth keeping up with events especially in the area of the world you are travelling in.
In most parts of the world at in the cities and large towns you will be usually able to get hold of local newspapers. Assuming you can read the local language these can make interesting reading but in a lot of countries they are heavily controlled by the government and therefore not tell the whole truth about developments in a particular country.
Western newspapers are often available in capital cities, tourist areas and the lobbies of business hotels they will usually be out of date by a couple of days and depending on the country you are in may not give any or at best limited coverage.
Depending where you are television may be available similarly to newspapers though language and government control might effect the usefulness of the information. In some countries different languages are used at different times of days or on different stations so try and get hold of a schedule or ask someone.
CNN however can be found in most business and a lot of tourist hotels all over the world. Often the televisions are in the lobbies or the lounges so assuming your smart enough then you can probably watch with out checking in although if its in a bar buying a drink might keep the owners happy! The main problem with CNN is that it is very American based and even if you are watching in Africa you are more likely to hear about a police shooting in New York rather than a massacre 100 miles away at your next destination.
Radio is probably the best means of gaining information while on the move. The main advantages are that you can get local and international broadcasts practically anywhere in the world, you can carry a radio with you and its also a good way to while away hours while waiting for a train.
The best type of radio to go is a shortwave radio these are available with analogue or digital tuning and can be as small as a cassette tape, although you will pay for the size. Typically for about £20 ($40) you can get a reasonable radio with analogue tuning which will give you FM, LW, MW and about 5 SW bands. Radio Shack (Tandy) used do one (Realistic DX-260) that had 6 SW bands and was about 2.5*8*15 cm in size which is pretty ideal. Sony do a very good small digital one costing about £200 ($400) but is a bit too tempting for thieves, officials etc.
Before you leave try and get a schedule for the part of the world you are heading for from one of the main world service providers. The international services tend to transmit exclusively on the SW bands. Probably the most well known and respected is the BBC World Service they have news, current affairs and an assortment of other programs specific the area they are transmitting to. Other stations worth checking out are Voice Of America (VOA) and your own countries.
Whichever station you choose to listen to you will find that the language and frequency they transmit on will vary depending on the time of day. It is therefore useful if you haven't got a schedule to note the day, time and frequency where you pick up a station.
When not listening to international services it worth having a tune around for local radio stations on FM, LW and MW that may be transmitting in a language you can understand. Again if you find one worth listening to note the day, time and frequency and don't be surprised if its not there next time you tune in.