Why are URLs not appearing in References with Bibtex?

The standard BibTeX styles do not support the field url or similar. If you need to include urls, you need to use a style which supports them. The urlbst package provides a way of converting a BibTeX style file into one which supports such fields. In particular, it provides pre-converted versions of the standard BibTeX styles. For example, \bibliographystyle{plainurl} or plainnat should give you a version of plain with the addition of support for fields like webpage, url etc.

As Mico noted, you may need to use biblatex given the entries in your .bib file. A simple example using the sample database provided with the package would be as follows:

\documentclass{article}
\usepackage{biblatex}
\addbibresource{biblatex-examples.bib}
\begin{document}
  \cite{ctan}
  \printbibliography
\end{document}

In this case, the compilation sequence is (pdf)LaTeX -> biber -> (pdf)LaTeX.

How to modify your MWE

This takes your code and demonstrates how to modify it to use biblatex. Some of the entry types you are using are actually unknown even to biblatex. (Perhaps they are intended for a specific style?) @electronic is known. I've declared @webpage and @url to be aliases of @online, which matches the way @electronic entries are handled. This will avoid the need to modify your .bib file while hopefully getting the entries handled in an acceptable way.

\documentclass[11pt]{article}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@webpage{TAPoverNabuccoDefeatEU,
    Date-Added = {2014-11-09 19:59:57 +0000},
    Date-Modified = {2014-11-09 20:01:28 +0000},
    Lastchecked = {September 21th, 2014},
    Month = {July},
    Title = {TAP Wins on Nabucco: A Total Defeat for the EU},
    Url = {http://eastbook.eu/en/2013/07/material-en/news-en/tap-wins-on-nabucco-a-total-defeat-for-the-eu/},
    Year = {2013}}

@electronic{NordStream,
    Date-Added = {2014-11-09 17:47:19 +0000},
    Date-Modified = {2014-11-09 18:23:12 +0000},
    Lastchecked = {Nov 11th, 2014},
    Title = {NordStream's official website},
    Url = {http://www.nord-stream.com/},
    Bdsk-Url-1 = {http://www.nord-stream.com/}}

@url{CIAnaturalGas,
    Author = {CIA},
    Date-Added = {2014-11-09 19:31:20 +0000},
    Date-Modified = {2014-11-09 19:32:46 +0000},
    Lastchecked = {September 13th, 2014},
    Title = {Country Comparison: Proved Natural Gas Reserves},
    Url = {https://www.cia.gov/library/publications/the-world-factbook/rankorder/2253rank.html},
    Year = {2014}}

@article{EnergyPoliciesReviewEU,
    Author = {International Energy Agency},
    Date-Added = {2014-11-09 20:42:47 +0000},
    Date-Modified = {2014-11-09 20:44:55 +0000},
    Lastchecked = {November 21th, 2014},
    Pages = {62},
    Title = {Energy Policies Review: The European Union},
    Url = {http://www.iea.org/publications/freepublications/publication/eu2008.pdf},
    Year = {2008}}

@url{PohjoinenLaivasto,
    Date-Added = {2014-11-09 17:53:07 +0000},
    Date-Modified = {2014-11-09 17:54:33 +0000},
    Lastchecked = {November 5th, 2014},
    Title = {Pohjoinen laivasto saa yli 40 alusta},
    Url = {http://finnish.ruvr.ru/news/2014_04_08/Pohjoinen-laivasto-saa-yli-40-alusta-6885/},
    Bdsk-Url-1 = {http://finnish.ruvr.ru/news/2014_04_08/Pohjoinen-laivasto-saa-yli-40-alusta-6885/}}
\end{filecontents}

\usepackage{biblatex}
\addbibresource{\jobname.bib}
\DeclareBibliographyAlias{url}{online}
\DeclareBibliographyAlias{webpage}{online}

\begin{document}
The Nord Stream \cite{NordStream}.
Vessels \cite{PohjoinenLaivasto}.
Gas to the TAP \cite{CIAnaturalGas, EnergyPoliciesReviewEU, TAPoverNabuccoDefeatEU}.

\printbibliography
\end{document}