I love my 2011 KLR, got it cheap about a year ago all farkled out. I will try to save you some pain:
Check your oil level at every fill up! These things are known to use oil at various levels, especially with extended riding at RPMs over 5k. 08s and some 09s are the worst.
If the bike still has the stock, slosh battery, get rid of it and get this:
http://www.batterymart.com/p-Big-Crank-ETX15L-Battery.html?Category_Code=kawasaki-kl650a-klr-battery
Also, do the doohickey upgrade ASAP using the Eagle Mike lever and torsion spring. No matter what you may hear, 2008+ KLRs require this. I have the tools, PM me if you want to borrow for postage.
Lube, with waterproof grease, in order of importance:
Unitrack bolt, unitrack bearings, swingarm bearings, R wheel and driven hub bearings, steering hub bearings.
Torque to spec all fasteners. The ones on the frame will be loose, I promise. Apply blue Loctite to all frame fasteners. Footpeg bolts torque to 18 ft/lbs (NOT 31 ft/lbs as per the shop manual). Safety wire on these is advised.
Clean and oil the air filter.
Check valves at 5k miles, then every 15k miles.
Change oil every 2k miles, filter every other oil change.
Suspension is OK to start with, but you will want to upgrade eventually. The front end is very soft.
If you off road, you will crash. Prepare for it with skid plate, racks, brush guards and crash bars. Mine are Happy Trails with Packrat pannier racks. You may need a low profile oil drain plug, depending on your skid plate.
Stock tires and seat are just awful.
Tires are all a compromise. Street/dirt 30/70 D606s are good, but expensive. 80/20 Shinko 705s are cheap and good. What I run.
I like Corbin seats.
Get yourself a shop manual but beware, there are errors in it!
For even more than you ever wanted to know about a KLR:
http://www.klr650.net/forums/index.php