I have to do a migration of my active directory to a new domain. I know that a lot of the SharePoint and SQL applications we run use domain accounts inside them and I'm worried how the migration will affect them. I'm assuming that as long as the account keep the same SID in the transfer I should be okay. Will it keep my SIDs the same?
An account cannot maintain its SID when it is moved between domains because the first portion of the SID is domain-specific. You can use the sIDHistory attribute to keep a list of old SIDs assigned to a user account inside the new user account object. Have a look at this document, it explains sIDHistory in the section "Migration with SID History":
The ADMT will only keep the SID history if you specifically tell it to do so when running the User Account Migration Wizard. See this kb article for additional information.
Since you are doing an intraforest restructure sid history is required. See ADMT v3.1 Guide: Migrating and Restructuring Active Directory Domains