You'll never believe it, but I replaced my 1994 325is battery for the FIRST TIME last week. That's 11 years of use. The "industry" suggests you change your battery every 2 years, but then the industry also sells batteries.
You will know when your battery needs replacing when it starts slow or doesn't start after sitting for a while. I used to store my car in the winter, and after sitting for 3 months it would require a jump. The car would run fine the remainder of the year.
This year I left the car for 5 days over xmas, and that was too much. It needed a jump, so I bought a new battery.
Your car shaking would not have anything to do with a dead/dying battery.
Past ownership: 1987 325is, 1988 325i, 1995 325is, 1996 325i Convertible, 1994 325is.
Current ownership (wife's): 2006 X3 3.0i
Future ownership: 3-series of some sort My office. My law blog.