One of the most common scams is that someone will offer you around 200k for your full rune set. You display the full rune and he shows the 200k in the trade window. Once you accept the trade, He will be sneaky and add in an extra item like black legs or something, and you'll think it's cool and accept the trade, and then boom! You had sold your full rune set for 20k and black legs.
You are now asking yourself, what had happened? Here is what happened. When he added on the black legs, he also took away 180k while you were looking at the black legs, and you didn't realize it cause 20k still looks kind of like 200k if you don't pay close attention.
If this ever happens to you report the scammer immediately.
Another Common Scam is that someone will be selling a rune 2 hander for 25k you will see the rune 2 hander in the trade window, and he will see the 25k, you will accept the trade and then he'll decline it saying, "Oops, my bad" and then he will trade you again offering a steel 2 hander or mith 2 hander, and then boom! You bought either a steel 2 hander or a mith 2 hander for 25k.
Other scams are that other people will offer free gem cutting or free smithing and then just take your items, and run. If he is a high level character than the odds are that he is not a scammer, but if he has low levels, then stay away from him.
Another Major Concern is Price Scamming; many people will scam your items for low prices. Especially with noobs, Check the forums for general prices before you sell something or ask around 1st.
Another Major Scam is that someone will offer to sell a Runescape account for Runescape gold coins or items. You will pay the player for the account, and he'll take off with your money. He will either give you nothing, or a username and password to a noob account he just created.
Another scam is that someone will want you to drop stuff during trades, only trade in the trade window.
Another Scam is that someone will tell you to drop something and hit alt+f4 to duplicate the item. All this does is closes your web browser and logs you out. And he will get the item that you drop.