These are the tips that I gathered from the excellent Chainsaw Safety Demonstration by our IDNR District Firester Jeff Harris at the end of August -

• keep your saw clean and the chain sharp
• file the raker blades when sharpening the chain's cutters
  
• use 91 octane ethanol-free gasoline
• wear protective clothing and accessories
  
• no one should be within reach when operating your saw
• when felling, everyone should be 2.5 times the tree's height away
  
• step back and estimate the weight or lean of the tree
• based on the lean, cut from the safe side, away from the lean
• spend the time to look for all the hazards
• plan two escape routes, each 45º off the intended tree fall
• your hinge width should be 80% of the DBH
• your hinge thickness should be less than 10% of DBH
• use an open-face/boring-cut technique
• if tree is thick enough, leave a rear trigger for release
• after cutting the trigger, always walk away on an escape route
  
• always keep both hands on the saw when it is running
• never cut across your body
• always engage the chain brake when walking or moving
• always lock your thumb on the front handle
• always quit when you feel tired

This isn't a comprehensive list and shouldn't be used as a substitute for professional training.  I'll expand this list based on any suggestions.