Standard European Political Landscape

Faction Calculus as applied to politics.

Most European nations have a multi-party political system, as a result of proportional representation; and even those countries which have a district system (such as Britain and France) tend to have more than two "significant" parties. And in just about all of them, you'll find several (and often all) of the following parties, in approximate order from Right to Left:

Far Right: A quite recent arrival in many countries. Far Right parties are a mixed bag, ranging from outright neo-Nazis who Put On The Reich to much more moderate groups. They are fond of simple, radical positions and strong language. They intensely dislike immigration, Islam, the European Union and the 'left-wing elite'. They are usually in favour of a tough approach to crime, and use nationalist and populist rhetoric. Interestingly, their economic programme is usually more left-wing than right-wing. Far Right parties attract many voters who are in some way dissatisfied with the more moderate, established political parties.
Classical Liberals: The primary defenders of capitalism and the free market. Usually popular among businesspeople and the upper class for this reason. This right-wing economic agenda is often coupled with a progressive stance on social issues like abortion, gay marriage and euthanasia, although in recent years, many Classical Liberal parties have moved to a more conservative position, especially when it comes to law and order.
Conservatives: The catch-all right-wing party. Best described as a fusion of the Christian Democrats (see below) and the Classical Liberals; they tend to have the economic agenda of the latter and the social agenda of the former. It is very important to note that a Conservative party will usually not thrive alongside any of these parties; in fact, a Conservative party can only flourish where Classical Liberal and Christian Democratic parties do not exist or are very small, and vice versa. Thus a European country will either have a Christian Democratic party and a Classical Liberal one (Germany, the Netherlands, Sweden) or a Conservative party (Britain, France, Spain). Switzerland does have a Conservative party alongside Christian Democrats and Classical Liberals, but it's quite small.
Christian Democrats: A party guided by Christian principles. They are often very close to the centre, although slightly to the right of it. They tend to have a moderately conservative position on social issues, but not a very clear economic agenda. Natural allies of the Classical Liberals, but they will also often work together with the Social Democrats (see below) in a "Grand Coalition". They're somewhat more uncomfortable when they have to work together with the Far Right, as has happened in the Netherlands.
Progressive Liberals: Somewhat rarer (and usually smaller) than any other type of party on this list, but they still show up often enough to be worth mentioning here. They have a very progressive stance on social issues and often a slightly-right-of-centre economic programme. They are also known for their fondness for electoral reform; many Progressive Liberal parties have 'Democratic' in their name for this reason, and indeed they are, in many ways, comparable to the Democratic Party in the US. They are often seen as sophisticated, nuanced and pragmatic; this image mostly attracts votes from the intellectual elite. A Progressive Liberal party will often work together with more or less anyone except the Far Right and the Far Left, but they're often especially cosy with the Greens, with whom they share their progressive social agenda.
Social Democrats: Almost always the principal left-wing party, and the direct opponents of the Classical Liberals. They will often have "Labour" or "Workers'" in their name, indicating their roots in the old struggle for high wages, decent working conditions and generous social security. They are clearly on the left, but not radically so, on both economic and social issues. Many of them made a move to the economic right in The Nineties (the "Third Way"), but most of them have returned to their left-wing roots since.
Greens: As the name implies, a party that cares a great deal about sustainability and the environment. This is usually coupled with a firmly left-wing (though not in a traditional way) economic agenda and a very progressive stance on social issues. Natural allies of the Social Democrats and the Progressive Liberals.
Far Left: A radically left-wing party which will defend the welfare state at all costs and doesn't trust businesspeople. They have more in common with the Far Right than either likes to admit; both "Far" factions share a fondness for populism and simplicity, and a distrust of the European Union. Both parties channel working-class discontent and rage, but whereas the Far Right directs this rage towards immigrants and left-wing intellectuals, the Far Left tends to direct it towards bankers, businesspeople and "managers".

Of course, these are not all present in every European country (some of them are even mutually exclusive, as pointed out above). Nor is it the case that there are no European political parties that do not correspond to any of these "types". But parties from this list do make up an overwhelming majority in just about every parliament in Europe, and dominate the political landscape of most European nations.

Also note that the parties can differ considerably in size. Traditionally, the Christian Democrats (or the Conservatives in countries which have them) and the Social Democrats are considered the "Big Two"; sometimes the Classical Liberals are also included, which gives us the "Big Three". Far Left and Far Right parties were often small before the Turn of the Millennium, but have now grown to medium size in many countries. The Greens and the Progressive Liberals are usually small to medium-sized.

Examples of Standard European Political Landscape include:

Austria

Far Right: Freiheitliche Partei Österreichs (FPÖ), except in Carinthia where they're called Die Freiheitlichen in Kärnten (FPK)
Classical Liberals: Bündnis Zukunft Österreich (BZÖ)
Christian Democrats: Österreichische Volkspartei (ÖVP)
Social Democrats: Sozialdemokratische Partei Österreichs (SPÖ)
Greens: Die Grünen - die grüne Alternative

Britain

Far Right: British National Party
Conservatives: Conservative Party
Progressive Liberals: Liberal Democrats
Social Democrats: Labour Party

Denmark

Far Right: Dansk Folkeparti
Classical Liberals: Venstre, Danmarks liberale parti
Conservatives: Det Konservative Folkeparti
Progressive Liberals: Det Radikale Venstre
Social Democrats: Socialdemokraterne
Greens: Socialistisk Folkeparti
Far Left: Enhedslisten

Finland

Far Right: Perussuomalaiset (PS)
Christian Democrats: Suomen Kristillisdemokraatit (KD)
Progressive Liberals: Kansallinen Kokoomus
Social Democrats: Suomen Sosialidemokraattinen Puolue (SDP)
Greens: Vihreä liitto
Far Left: Vasemmistoliitto

France

Far Right: Front National (FN)
Conservatives: Union pour un Mouvement Populaire (UMP)
Progressive Liberals: Mouvement démocrate (MoDem)
Social Democrats: Parti Socialiste (PS)
Greens: Europe Écologie - Les Verts (EELV)
Far Left: Front de Gauche

Germany

Classical Liberals: Freie demokratische Partei (FDP)
Christian Democrats: Christlich demokratische Union Deutschlands (CDU), except in Bavaria where they're called the Christlich-soziale Union in Bayern (CSU)
Social Democrats: 'Sozialdemokratische Partei Deutschlands (SPD)
Greens: Bündnis '90/Die Grünen
Far Left: Die Linke

Greece

Far Right: Chrysi Augi
Conservatives: Nea Demokratia (ND)
Social Democrats: Panellenio Sosialistiko Kinema (PASOK)
Far Left: Synaspismos Rizospastikis Aristeras (SYRIZA)

Italy

Far Right: Lega Nord (LN)
Classical Liberals: Popolo della Libertà (PdL)
Christian Democrats: Unione di Centro (UdC)
Progressive Liberals: Italia dei Valori (IdV)
Social Democrats: Partito Democratico (PD)

The Netherlands

Far Right: Partij voor de Vrijheid (PVV)
Classical Liberals: Volkspartij voor Vrijheid en Democratie (VVD)
Christian Democrats: Christen-Democratisch Appél (CDA)
Progressive Liberals: Democraten '66 (D66)
Social Democrats: Partij van de Arbeid (PvdA)
Greens: GroenLinks
Far Left: Socialistische Partij (SP)

Norway

Far Right: Fremskrittspartiet (FrP)
Classical Liberals: Høyre
Christian Democrats: Kristelig Folkeparti (KrF)
Progressive Liberals: Venstre
Social Democrats: Arbeiderpartiet
Far Left: Sosialistisk Venstreparti (SV)

Russia

Far Right: DPNI ("the Movement to Counteract Illegal Immigration", an outlawed party)
Classical Liberals: Right Cause (a dwarf party), Another Russia (an outlawed one too)
Conservatives: United Russia
Progressive Liberals: Yabloko (Apple Party)
Social Democrats: A Just Russia
Far Left: Left Front (an outlawed party)
Don't Fit In: Communist Party of the Russian Federation (a blend of social-democrat and conservative), Liberal Democratic Party of Russia (looks like far-right, but in fact populist all bark and no bite).

Spain

Conservatives: Partido Popular (PP)
Progressive Liberals: Unión Progreso y Democracia (UPyD)
Social Democrats: Partido Socialista Obrero Español (PSOE)
Far Left: Izquierda Unida (IU)

Sweden

Far Right: Sverigedemokraterna (SD)
Classical Liberals: Moderata samlingspartiet
Christian Democrats: Kristdemokraterna (KD)
Progressive Liberals: Folkpartiet Liberalerna (FP)
Social Democrats: formally Sveriges Socialdemokratiska arbetarparti (SAP), more commonly known as Socialdemokraterna
Greens: Miljöpartiet de gröna (MP)
Far Left: Vänsterpartiet

Switzerland

Far Right: Schweizerische Volkspartei (SVP)
Classical Liberals: FDP.Die Liberalen
Conservatives: Bürgerlich-Demokratische Partei (BDP)
Christian Democrats: Christlichdemokratische Volkspartei (CVP)
Social Democrats: Sozialdemokratische Partei (SP)
Greens: Grüne Partei