There are more than 20 (perhaps more than 30) political parties in Brazil, but just some of them are relevant. Most of them were created or recreated when the military rule ended in the 80's.
The largest and most relevant parties are:
1. The Worker's Party, known as PT or Partido dos Trabalhadores. It was created by leftist union leaders from Sao Paulo. It's the Brazilian ruling party since 2003, when it abandoned its far left agenda and adopted a pragmatic approach to the economy.
2. The Brazilian Social Democracy Party, known as PSDB or Partido da Social Democracia Brasileira. It was created by leftist intellectuals from Sao Paulo. It was the Brazilian ruling party from 1995 to 2002, when it adopted a conservative agenda and stabilized the Brazilian currency.
3. The Brazilian Democratic Movement Party, known as PMDB or Partido do Movimento Democatico Brasileiro. It comes from the MDB, the center-left political party that opposed the military rule from 1964 to 1985. It's a large federation of regional politicians and interests, without well defined, nationwide positions or ideology. It was the Brazilian ruling party from 1985 to 1989, when it peacefully conducted the transition to democracy while Brazil was experiencing a hyperinflation crisis. From 1990 until now, it has supported the ruling party, whichever it may be.
4. The Democrats, known as DEM or Democratas. It comes from the UDN, a conservative party from the 50's, and ARENA, the ruling party during the military rule, from 1964 to 1984. It has been a PSDB ally since 1994.
Some curiosities about Brazilian political parties:
1. PPS, formerly known as PCB, the Brazilian Communist Party, changed its name to Popular Socialist Party and now is a conservative party!
2. A new PCB was created some years after the former PCB changed its name.
3. The Sao Paulo mayor has just created his own party, PSD. It seems its faith is to become a tiny party.
4. Many tiny parties have no ideology and it is believed they can be hired for money. This is the essence of the Mensalão scandal, now being tried.
5. There is no equivalent to the GOP in Brazil. Even the most conservative Brazilian party would be labeled as leftist in the US.
6. The president of the federation of industries of Sao Paulo belongs to the Brazilian Socialist Party (PSB).
7. The mainstream media from Sao Paulo and Rio support the PSDB.
And now, several lists of Brazilian political parties. Enjoy!
Some midsize Brazilian parties: PSB, PTB, PPS, PDT.
Some Brazilian left wing parties: PSTU, PCO, PSOL, PCB, PCdoB.
Some Brazilian conservative parties: DEM, PSDB, PPS.
Some Brazilian center left parties: PT, PSB, PDT, PV.
Some Brazilian center or non ideological parties: PMDB, PTB, PP, PSD, PHS, PSC, PMN, PRB, PTdoB, PTN, PRP.
Some Brazilian tiny parties: PSTU, PCO, PSOL, PCB, PCdoB, PP, PSD, PHS, PSC, PMN, PRB, PTdoB, PTN, PRP, PV.