exporting to shapefiles

A simple way to do this is using Overpass Turbo. For example, this query was generated using the Assistant and typing "power=tower in Oman". You can easily adapt the query to get the lines themselves. Just check the wiki to see what exactly you need. You can then export the data to GeoJSON, which you can drag and drop to QGIS. If you really want to use shapefiles, you can simply save as shapefile in QGIS. There is built in support in QGIS (and also the QuickOSM plugin) to do the same without going over a website.

Of course, if you want to do something more advanced, Jochen's answer is more interesting.

There are many ways of doing this, they all have their advantages and disadvantages. A lot depends on the amount of data you are dealing with (whole planet vs. small extract) and the system and skills you have. If you are familiar with SQL/PostGIS, for instance, you can use one of the PostGIS importers (like osm2pgsql or imposm) to import OSM data into a PostGIS database and then export into Shapefiles. If you like command lines, try ogr2ogr. If you need something more custom and know C++, you can write your own exporter based on https://github.com/osmcode/osm-gis-export. For smaller files, you can build something with use node-osmium, see the demo here: https://github.com/osmcode/node-osmium/tree/master/demo/converter.

http://wiki.openstreetmap.org/wiki/Shapefiles has more options.

A little bit more explanation to @joost-schouppe answer. First you need to find out "Oman" or any other region's OSM relation id.

Use this query in Overpass Turbo

[out:json][timeout:900];
// get a few areas into .myArea
// you can add or remove an area by simply adding or removing
// one line here.

(
{{geocodeArea:"Oman"}};
)->.myArea;

// display .myArea This can be replaced by any query
// on the objects in .myArea

rel(pivot.myArea);

// print results
out geom;

{{style:
node{opacity:0;fill-opacity:0}
}}

Now once you know the OSM relation id then you can extract any layer easily with overpass API. OSM relation id for "Oman" is "305138"

Here is curl command to extract power line using Area clause of overpass API

curl \
  -H "Host: overpass-api.de" -H "Content-Type: text/xml"  \
  -d '(relation["route"="power"](area:3600305138););(._;>;);out body;'  \
  http://overpass-api.de/api/interpreter  \
  -o powerline.osm

Now you can use ogr2ogr to convert OSM to shapefile.