When you work for yourself, fearing that you may run out of work or that you might not have enough money to pay your bills is normal. Most freelancers feel this way at one point or another, especially when you lose a client or two.
However, your fear can be transformed into the desire to please your clients at all costs including accepting tasks that you wouldn't normally consider doing and doing work for free. This is especially easy to do when you have new clients who seem to have increasing expectations. Rather than risk losing the client (and the income you earn from him), you may just begrudgingly accept the additional tasks without saying anything. This is almost always a mistake.
First, recognize that the fear of not having enough income is natural, but it doesn't mean it's valid. After all, you were able to secure clients initially, and with good marketing, you can find additional clients. (Read Free Marketing Tips you May Not Have Tried for additional ideas!)
Second, you train the clients how you'd like to be treated. If you have a contract with a client with clearly defined tasks and the client asks you to do additional work, you need to decide how you'd like to be treated. You can just meekly accept the extra work, which will train the client to understand that you will do what is asked without question.
Alternatively, you can accept the extra work but negotiate how much you'll be paid for these tasks. This is generally the best solution as it shows the client that you're flexible and can accept additional tasks when necessary. Doing so will also train the client that you believe you should get paid what your time is worth. (See How to Raise Your Rates without Losing Clients for more info.)
The last way to handle extra requests is to just say no. If you are too busy to accept the work, saying no is better than accepting the work and being unable to complete it in a timely manner. However, if you have time, accept the work and negotiate for additional pay.
You teach your new clients how to treat you. Try to put your fear of not earning enough income aside so you can negotiate and get paid what your time is truly worth.