Open box spanners: (I prefer them to double rings as the double rings always come in the wrong combination of sizes with one end you'll never need)
10mm, 12mm, 13mm (only if you have nylocs on your drivechain tensioners), 14mm, 19mm, 22mm, 24mm (or 27mm depending on what KLR you have)
Allen 6mm for handlebar cap screws and brake calipers.
Add 3mm, 4mm and 5mm if you replaced all the crappy Philips bolts with allen head caps and button heads (you should!)
Sockets 8mm and 10mm plus a ratchet and extension.
Philips screwdriver in case you have any Philips scrap left on the bike (you shouldn't)
Spark plug wrench
besides that the usual: 2 tyre levers (passenger car size), bottle with soapy water, inner tubes, patches, pump, plenty of cable ties, tie downs, duct tape...