Pull Ups: If you can't do pull ups, or don't have the equipment to do pull downs, you can replace them with another pulling or upper back exercise like rows. You can also use rubber tubing. (FX Day 3)
Sand Bag Slam: If you don't have a sand bag, you can use a medicine ball, or make a heavy slamming object with old rags wrapped up in duct tape. You can place something heavy in the middle to make the exercise more demanding. The sandbag I use in my FX Boot Camp is currently about 35 lbs. (FX Day 12)
Bench Crawl: You don't necessarily need to crawl under a bench, you can just crawl for a short distance. (FX Day 6)
For any exercise that requires dumbbells, you can either use a barbell or heavy water jugs. You can also use dumbbells instead of a barbell. (FX Day 2)
Don't let the lack of equipment stop you from getting in a good workout, burning the fat and losing that unwanted weight. Be creative. There's all kinds of things you can use to add resistance.