The answer is either 981 million or 2.3 billion, depending on whether you include Chinese. Out of 6.697 billion people in the world as of this writing (see http://www.google.com/publicdata?ds=wb-wdi&met=sp_pop_totl&tdim=true&dl=en&hl=en&q=world+population ) this means either 14.6% or 34.4%. Note that there could be some double-counting where some people speak more than one of the languages written from right to left (e.g. Hebrew and Arabic), so the above should be taken as a rough approximation.

Lets' start by enumerating the languages this includes. According to http://www.omniglot.com/writing/direction.htm#rtl these are:

- quote -
Ancient Berber, Ancient Egyptian (Demotic), Ancient Egyptian (Hieratic), Ancient Egyptian (Hieroglyphic), Aramaic, Arabic*, Avestan, Chinese **, Cypriot, Enochian, Etruscan, Hebrew, Iberian (Northern), Kharosthi, Linear B, Old Italic, Orkhon, Mandaic, Mende, Meroïtic (Cursive), Middle Persian, Nabataean, N'Ko, Parthian, Phoenician, Proto-Elamite, Psalter, Sabaean, Samaritan, Sogdian, Tifinagh, Syriac, South Arabian, Thaana
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Many of these are no longer in current use except possibly by a few scholars, so I'll ignore them.
Aramaic - spoken by only a small number of people, so I'll ignore it in the following.
- quote (http://www.omniglot.com/writing/aramaic.htm ) -
Aramaic was once the main language of the Jews and appears in some of the Dead Sea Scrolls. It is still used as a liturgical language by Christian communities in Syria, Lebanon and Iraq, and is still spoken by small numbers of people in Iraq, Turkey, Iran, Armenia, Georgia and Syria.
- end quote -

Arabic - 221 million speakers
- quote (http://www.omniglot.com/writing/arabic.htm ) -
Arabic is a Semitic language with about 221 million speakers in Afghanistan, Algeria, Bahrain, Chad, Cyprus, Djibouti, Egypt, Eritrea, Iran, Iraq, Israel, Jordan, Kenya, Kuwait, Lebanon, Libya, Mali, Mauritania, Morocco, Niger, Oman, Palestinian West Bank & Gaza, Qatar, Saudi Arabia, Somalia, Sudan, Syria, Tajikistan, Tanzania, Tunisia, Turkey, UAE, Uzbekistan and Yemen.
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Chinese - 1325 million (see http://www.google.com/publicdata?ds=wb-wdi&met=sp_pop_totl&idim=country:CHN&dl=en&hl=en&q=population+of+china )

- quote (http://www.omniglot.com/writing/chinese.htm ) -
Traditionally Chinese was written from right to left in vertical columns. The first publication in Chinese using horizontal (left to right) text was Robert Morrison's Dictionary of the Chinese language, published in 1815–1823 in Macau. The increasing use of words in Western languages, especially English, in Chinese texts from the early 20th century made horizontal texts more popular.

Since 1949 horizontal writing has become the standard in the PRC, and all PRC newspapers changed from vertical to horizontal text in 1956, though some headlines are written vertically, as are inscriptions of signs on most state organisations.
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Hebrew - 8 million

- quote (http://www.omniglot.com/writing/hebrew.htm ) -
Today Hebrew is spoken by some 5 million people in Israel, where it is an official language along with Arabic. and a further 2 to 3 million people speak the language in Argentina, Australia, Brazil, Canada, France, Germany, Palestinian West Bank and Gaza, Panama, the UK and USA.
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N'Ko alphabet (used to write Mandekan) - 5 million

- quote (http://www.omniglot.com/writing/nko.htm ) -
Mandekan, a member of the Mande group of Niger-Congo languages spoken by about 5 million people in Mali, Senegal, Guinea, Ivory Coast, Burkina Faso and Sierra Leone. Mandekan, which is also known as Manding or Mandingo, is actually a group of closely related dialects, including Bambara and Dyula, which some linguists classify as separate languages.
- end quote -

Syriac alphabet (used to write Neo Aramaic) - 0.2 million

- quote (http://www.omniglot.com/writing/syriac.htm ) -
Assyrian Neo-Aramaic, a diverse group of Eastern Aramaic/Syriac dialects spoken by about 200,000 people mainly in Iraq, Syria, Iran, Armenia, Georgia and Turkey.
- end quote -

Thaana alphabet (used to write Maldivian) - 0.3 million

- quote (http://www.omniglot.com/writing/thaana.htm ) -
Dhivehi (Maldivian), an Indo-Aryan language spoken by about 300,000 people in the Maldives and on India's Minicoy Islands.
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Arabic characters are used in other languages ("Used to write: Arabic, Baluchi, Dari, Hausa, Kabyle, Kashmiri, Kazak, Kurdish, Kyrghyz, Malay, Morisco, Pashto, Persian/Farsi, Punjabi, Sindhi, Siraiki, Tatar, Turkish, Uyghur, Urdu and a number of other languages" according to http://www.omniglot.com/writing/arabic.htm ):

Baluchi - 7 million
- quote (http://www.omniglot.com/writing/baluchi.php ) -
Baluchi is a Northwestern Iranian language spoken by about seven million people.
- end quote -

Persian or Farsi - 130 million

- quote (http://www.omniglot.com/writing/persian.htm ) -
Persian is a member of the Iranian branch of Indo-European languages spoken by about 130 million people, mainly in Iran, Afghanistan and Tajikistan.
- end quote -

Hausa - 39 million

- quote (http://www.omniglot.com/writing/hausa.htm ) -
Hausa is a Chadic language with about 39 million speakers. It is spoken mainly in northern Nigeria and Niger, and also in Benin, Burkina Faso, Cameroon, CAR, Chad, Congo, Eritrea, Germany, Ghana, Sudan and Togo.
- end quote -

Kabyle - ~7.5 million

- quote (http://www.omniglot.com/writing/kabyle.php ) -
Kabyle is a Berber language with about 7-8 million speakers, most of whom live in Algeria, mainly in Kabylie in the north of the country.
- end quote -

Kashmiri - 4.5 million

- quote (http://www.omniglot.com/writing/kashmiri.htm ) -
Kashmiri or Koshur is an Indo-Aryan language with about 4.5 million speakers in India, Pakistan and the UK. The Kashmiri alphabet was adopted from the Urdu version of the Arabic script.
- end quote -

Kazakh - 8 million

- quote (http://www.omniglot.com/writing/kazakh.htm ) -
Kazakh or Qazaq is a Turkic language spoken in Kazakhstan, Russia and China by about 8 million people.
- end quote -

Kurdish - 26 million

- quote (http://www.omniglot.com/writing/kurdish.htm ) -
Kurdish is a member of the Western Iranian branch of Indo-European languages. Approximately 26 million people speak Kurdish in Iraq, Turkey, Iran, Syria, Lebanon, Armenia, Georgia, Kyrgyzstan, Azerbaijan, Kazakstan and Afghanistan
- end quote -

Kyrgyz - 1.5 million

- quote (http://www.omniglot.com/writing/kirghiz.htm ) -
Kyrgyz or Kirghiz is a Turkic language with about 1.5 million speakers in Kyrghyzstan and China.
- end quote -

Malay/Indonesian - 188 million

- quote (http://www.omniglot.com/writing/malay.htm ) -
Malay is an Austronesian language spoken in Malaysia, Indonesia, Singapore, Brunei and Thailand. The total number of speakers of Standard Malay is about 18 million. There are also about 170 million people who speak Indonesian, which is a form of Malay.
- end quote -

Pashto - ~50 million

- quote (http://www.omniglot.com/writing/pashto.htm ) -
The exact number of Pashto speakers is not known for sure, but most estimates range from 45 million to 55 million.
- end quote -

Panjabi - 60 million

- quote (http://www.omniglot.com/writing/gurmuki.htm ) -
Panjabi or Punjabi, an Indo-Aryan language spoken by about 60 million people in Pakistan and the Indian state of Panjab.
- end quote -

Sindhi - ~20 million

- quote (http://www.omniglot.com/writing/sindhi.htm ) -
Sindhi is an Indo-Aryan language with about 17 million speakers in the south-eastern province of Sind in Pakistan and about 2.8 million people in India.
- end quote -

Siraiki - 14 million

- quote (http://www.omniglot.com/writing/siraiki.htm ) -
Siraiki is a member of the Indo-Aryan branch of Indo-European languages and spoken by about 14 million people in the central Pakistan provinces of Sindh and Punjab.
- end quote -

Tatar - 7 million

- quote (http://www.omniglot.com/writing/tatar.htm ) -
Tatar is a Turkic language with about 7 million speakers in Russian republic of Tatarstan, and also in Afghanistan, Azerbaijan, Belarus, China, Estonia, Finland, Georgia, Kazakhstan, Kyrgyzstan, Latvia, Lithuania, Moldova, Tajikistan, Turkey (Europe), Turkmenistan, Ukraine, USA and Uzbekistan.
- end quote -

Turkish - 70 million

- quote (http://www.omniglot.com/writing/turkish.htm ) -
Turkish is a Turkic language with about 70 million speakers in Turkey and in 35 other countries, including Australia, Austria, Azerbaijan, Belgium, Bulgaria, Canada, Cyprus, Denmark, El Salvador, Finland, France, Georgia, Germany, Greece, Honduras, Iran, Iraq and Israel.
- end quote -

Uyghur - 10 million

- quote (http://www.omniglot.com/writing/uyghur.htm ) -
Uyghur is a Turkic language with about 10 million speakers mainly in the Xinjiang Uyghur Autonomous Region of China, and also in Afghanistan, Australia, Germany, India, Indonesia, Kazakhstan, Kyrgyzstan, Mongolia, Pakistan, Saudi Arabia, Taiwan, Tajikistan, Turkey, the USA and Uzbekistan.
- end quote -

Urdu - 104 million

- quote (http://www.omniglot.com/writing/urdu.htm ) -
Urdu is an Indo-Aryan language with about 104 million speakers, including those who speak it as a second language.
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Most languages that are written right to left are what as known as Semitic languages. About 6% of the world population or 467 million people speak these languages.

Interestingly enough, Japanese is usually written vertically, but when written horizontally it is written left to right, except before WWII, when it was right to left.

Hebrew mentions only 5 million of Hebrew speakers in Israel and 3 million scattered in the world. Yet, there are 7 million inhabitants in Israel, and even those who are not really fluent in Hebrew probably speak it beter or as well as those living in other countries and registered as Hebrew speakers.
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