Congratulations on your purchase of the CONSOLE KING!
No, It doesn't have a built-in Hard Drive to save anything.
It's natural to be slow on anything in this world in the beginning, but slowly as we get used to it, we just fly with it! So do not worry and feel free to ask, I will help in the best possible manner because I myself have faced many issues and found answers to all my PS2 queries.Thanks to the GREAT INTERNET!
ABOUT MEMORY CARD:
Sony doesn't include memory card in the package which is really very bad, because you won't like to play any game again and again from the start like an 8-bit Video Game!
And PS2 games are not so small that you can afford to start and sit at a stretch and complete the entire game in one shot!
Besides you need to give some rest to your PS2.
So, I would say that you cannot do without a memory card, if you wish to complete any game!
If you just wish to see how the game looks and just want to feel it, then you can do without memory cards, but as previous answerers said, some games do not budge without memory card!
So it's a good idea to have a memory card which is available freely all over the internet at a very low cost of as low as $ 8!
Try http://www.dealextreme.com/
they offer worldwide free shipping! And it's reliable, believe me!
You will feel relaxed when you save your games and turn off your PS2. So go get it!
PS2 WROX!