What was the last, if any, maintenance, repair work, upgrade, modification, etc, that you did to the bike? This is always a good place to start when troubleshooting.
Does your bike have "after-market" handlebars (or have the bars been changed/replaced at some time in the past)? If so, this too would be a very good place to start your troubleshooting (certain HD bar/wire systems are very prone to pinched wires and short circuits).
You can also test for excessive parasitic draw by try the following (in addition to GotGold's suggestion):
1. Turn off both the key and the "run/start" switch.
2. Disconnect the battery negative cable (be sure to follow "misinlink's" and "Shmidty's advice).
3. Place a 12 volt test light between the disconnected battery neg. cable terminal and ground.
A. The test light should be pretty dim, or off entirely. If it's pretty bright, then suspect excessive parasitic draw. Note: you can test the "relative brightness" of the test light by connecting it directly to the battery terminals. You, of course, can also use a properly ranged amp meter (in place of the test light) for accurate parasitic amperage draw readings. You can consult your HD service manual and/or your HD service tech for the maximum allowed amperage draw. This will be expressed in "milliamps"
(i.e. one thousandth of an amp).
Continue the test by turning on the "run/start" switch while the key is still in the "off" position. See "A" above.
Also be aware that many Sportsters are known for developing corrosion problems on various electrical connectors (i.e. circuit breakers, fuse blocks, wiring, grounds, etc). A thorough cleaning/tightening and an application of dielectric grease can greatly reduce this problem (as others have probably mentioned).
Here's a link that can help with general motorcycle electrical troubleshooting:
The Motorcycle Electrical Diagnosis:
How to diagnose electrical problems, charging system on your motorcycle