The answer to this question is dependent on where you plan to vote. There are a number of different styles of primary, ranging from closed primaries, in which you must be registered with a political party to vote, to open primaries, in which voters may vote for any candidate from any party. Because primary elections are extremely complex and quite varied, you may want to check with your local government before you vote in the primaries of your region. Typically a registrar of voters will be able to provide information about which primary system is used in your region.
You are not usually required to register with a political party when you file voter registration paperwork. People who do not wish to be affiliated with a particular party can indicate that they are “non-partisan.” However, when you vote in the primaries, your party affiliation may determine which ballot you get. In a region with a totally closed primary system, non-partisan voters may not have any say in candidate nominations, and people with party affiliations must vote the ballots of their parties. A member of Party A, for example, may not vote the ballot of Party B.
In a closed primary, voters must be registered with specific political parties to be allowed to vote. Each party provides its own ballot, which includes the name of proposed candidates. If ballot measures have been added to the ballot, they will appear on the ballots of all parties. Voters may also vote in the primaries by attending caucuses, conventions, or nomination meetings; as a general rule, one must be registered with a particular party to attend its caucus or convention.
In many regions, governments hold what are known as “semi-closed” primaries. In these primaries, someone who is not registered with a political party can request the ballot of a specific party. Not all political parties will allow non-partisan voters to vote on their ballots; in many parts of the United States, for example, non-partisans can request a Democratic ballot, but not a Republican one. If you are an absentee voter, you will need to request a ballot for a specific party ahead of time, or the local government will send you an non-partisan ballot.
In the case of an open primary, voters can request a ballot for any party when they reach the polls. Some regions hold blanket primaries, in which all candidates from all parties are listed on a single ballot, and voters pick one per office. These types of primaries are relatively rare, out of concerns that people could potentially sabotage the nominations of opposing parties by voting for their weakest candidates.
Your vote in the primaries can be important, which is why it is a good idea to find out exactly what kind of primary is held in your region. If you wish to vote in the primaries in a region with a closed primary system, you should probably register with the party which has values which are most closely aligned with yours. If you like in a region with a semi-closed primary, check to see which parties will allow you to vote their ballots if you wish to register as a non-partisan, because you do not want to end up with limited choices at the polls.