That depends where your at, Some guys can barely do any pushups at that point yes they will do quite alot for someone that doesn't want to get at all serious about lifting. Using all the different variations (wide close ect..) you can target chest/tris, and w/ some dumbbells you can incorporate quite alot of other excercises.
If you don't want to buy many weights get some dumbells. After pushups become to easy you can further train chest using your dumbbells that you also use for bis/tris. via, flys the torque will make those little dumbbells give alot of weight onto your chest if your arms are nearly all the way extended out. Chins and pullups can go a long way for a good back, you don't tend to grow out of doing them very easily, if you do you can use a rope and wrap it around your legs (bend your legs to hold onto the rope) and put the weight on the other end. Works great considering chins are hard to beat as a back excercise even when you are a member to a full blown gym. Basically most excercises have variations that make them harder you want to look into what makes them hard to perform, since that way you can use the fewest amount of weights and cover the largest basis.
Example,
Get a pair 25IB and a 35IB dumbbells
day1.
Chest/Tris.
Pushups (unless that become so easy its stupid)
Flys, remember you can greatly vary the amount of weight used in these by the spread of your arms (torque) I.g. if you just do it like a dumbbells press its going to be way to easy however if you've got a complete spread on your arms out to the side its much harder). It helps to either do these on a bench or one the ground w/ some pillows under your back so that your elbows if need can drop below your shoulder line
Kickbacks
Skull Crushers
day2.
back/bis
Chins/pulls ups (w/ or w/o weights)
curls
(any simple variations of the two)
day3.
Shoulders/abs
dumbbells shoulder press
can't think of there name put the damn things whereit looks like your trying to take flight, these will work quite well with limited weights again because of torque.
crunches/reverse crunches
weighted crunches
day4.
legs
This one is kind of a bitch you can't do to much w/o having to much weight. Basically you can do lunges holding the dumbells, that way since it only works each leg at a time the leg is forced to carry more weight.
calve raises, get a block and a tall chair, stand on the edge of the block w/ only one foot hold a weight in the hand of the foot side you are working use the other hand on the chair to stablize your self. (other option is to hold a weight in each hand and spring upwards actually like jumping but w/o bending your knees (except mabe a little for landing so you don't hurt your self) basically your using the extra force that is placed on your calves for exceleration. This can also be done 1foot at a time to increase difficulty (to be honest its hard to add size to calves, this isn'y going to help you add 10IBs much)
Just to warn you, if you manage to gain 10 decent pounds, you won't stop your going to get a gym member hip or start building your self a decent stock of equipment ITS ADDICTIVE! have fun