Anything that doesn't pose a choking hazard and isn't a known family food allergen is OK according to the American Academy of Pediatrics.
They have a parenting website, HealthyChildren.org, that has great resources including a sample menu for a child that age:
http://www.healthychildren.org/English/ages-stages/baby/f...
My kids loved fresh fruit (blueberries, strawberries, grapes, bananas, pear slices, apple slices, etc), yogurt, toast, oatmeal, eggs. I was always there and felt comfortable giving them larger pieces to help them learn to chew. So, bananas, I'd give them 1/2 a banana and let them gnaw on it, same with thin slices of apples/pears that they could chew.
Of course, verify our advice with your pediatrician, but anything goes!