When a project closes during your current year, you can mark it as completed and archive it. I don't like archiving projects since I want to reference all the information for reports. Daptiv has added some functions allowing reporting on archived projects, but if you want to work with a project once archived, you have to reactivate it before you can work on it. I normally just change the status to Completed and filter out this status on most views. I like projects available for a year for reporting before "hiding" them by archiving them.
If a project is going to carryover from this year to next, I have two choices:
1) Close out the project this year and have full accounting for finanials and other metric and then present the carryover project as a new project for next year to be considered and scored alonside all proposed and active projects (this is a good time to re-evaluate if this is a good project to do and clean house if necessary). I like closing the books at the end of the year and scoring active projects alongside proposed projects for the new year.
2) Treat the project as a multi-year project and keep tracking things. The problem with this choice is it makes it hard to tie financials to fiscal years (if your fiscal year is off of the calendar year, you may want to make these changes with your fiscal year).
If you are worried about having the deal with project carryover on multi-year projects, manage your projects on a month-by-month basis and close the books and status each month. This is a great time for your Governance group to evaluate the performance of the project team and evaluate if the project is still viable and the same priority.