Allegiant offers discounted fares but then makes their money off of the fees. They charge for a seat assignment, they charge per bag, they charge $15/person to book over the internet. Once on board, they don't offer free drinks but charge for drinks and snacks, etc.
You can get around most of the fees. The $15 charge to book over the internet can be waived if you book at one of their counters in the airport. You can decline to purchase a seat assignment. However, if you have a child, there is no way to guarantee you'll be seated together. They board in order of first boarding those with a seat assignment. Then, they do general boarding. The earlier you check in, the lower the number you will be given for general boarding. They generally board 1-25 and then 26-50. Then they alllow all people with children 8 or younger to board the plane, regardless of boarding number, so they can attempt to sit together. Depending on how many preassigned seats were sold, you may sit together, you may not. After that, they board the rest of the plane based on boarding number again.
You can also get around paying for luggage if you only bring a carry-on but be warned they are VERY strict with the size. If your bag is too big they will make you check it and it costs more to check it at the gate than to pre-pay to check it. Also be aware they almost always run out of overhead bin space, so if you have a late boarding number, you may have to check your bag anyways (but they don't charge you if they run out of space.)
They are a smaller airline and their seats and space feel the smallest to me out of any airline, so because of this, we will only fly them for short flights. I couldn't imagine taking a long flight with them, but this is just my opinion.