It depends on how you're migrating the databases. If you are attaching them or restoring from backup they will still hold their collations. If you need to change them you can do so from SSMS. Right click the DB, Properties then Options. But if these databases are connected to applications they will likely have this custom collation for a reason & you shouldn't change it.
The instance collation is there for new databases & your system databases.
If you do have databases with a different collation than the instance you can encounter problems when using the tempdb for example
IE. If you create a temp table, it will take on the system database collation. If you then compare some column in that temp table with a column in one of your databases you can encounter a "collation conflict" error.
There are ways around it by specifying collation when creating the temp table but its something to be aware of at least.