If a Queen is a Rook + Bishop, why isn't it worth 8 points?

Because having both powers means more flexibility and mobility.

Try putting a rook and a bishop on the same square !

The whole is greater than the sum of its parts.

A queen can control files and diagonals at the same time. Also, maybe you can say the queen counts as a bishop pair (which can be worth a pawn in an endgame) as it can switch from black to white squares.

Actually this is pretty new to me. I was always told that a Queen=10. Another interesting question is: what is more powerful, 2 Rooks or a Queen? It is generally accepted that 2 Rooks are stronger than a Queen, but personally I think that it is open for debate

I think the closer you get to the endgame, the stronger the rooks are vs the queen.

Kaufman would agree with you that the Queen = 10.  He'd also say that rooks are 5.25 and minor pieces are 3.5. :)

Pardon my ignorance, but I have never understood the need for  numerical values of chess pieces. I mean, what's the relevance? Besides it totally depends on the position. Two queens are surely stronger than two pawns, but what if the pawns are on the right squares to give a mate in 2 with the aid of a good lone king?  Or this: I cannot imagine a single player saying ok I'm gonna totally resign now 'cause it's ike 21 points of material down.

I can totally understand general chess rules, the famous don't move the same piece in the opening twice, try to control the center etcetera...and these two can be broken a lot of times too. But numerical value of a piece it's so nonsense to me.

Maybe it's helpful or 100% needed when programming a chess engine? I don't know.

   The relevance of numerical values is very helpful during a game to know if you are ahead or behind in material and by how much. This allows the player to assess whether or not to take risky or defensive moves. Also it helps in determining whether trading may or may not be helpful

   I'm not saying that you can't be down on material but be in a better strategic or tactical position. We all know (and I've been in this position quite a few times) that a player can be down a Q and still win. But what I am saying is that counting material is a useful tool.

   For example, if we are getting toward the end game, I don't want to be down one point against a peer. Or, if I am up a piece in midgame, I might want to start trading down.

   I play games with friends who refuse to pay attention to the material count. They are always quite low level players who can't be bothered and don't comprehend the reasons.

   This is not poker where Kenny Rogers sings "...don't count your money 'til the game is done". This is chess.

   btw, I am not a card player but I would still want to have an approx. idea of wheter I was ahead or not, but I wouldn't be obvious about it. Nice song, though.

   Kenny Rogers:

When you're sittin' at the table
There'll be time enough for countin'
When the dealin's done

Synergy.

I think it has to do with the fact that it can move to different colored diagonals (it can take on the job of the LSB or DSB) which is worth more than one Bishop.

For me it's more like I don't want to be down a pawn, or a minor piece, or with a bad bishop vs a good knight and so on. To each his own!

You can't move a bishop and a rook at the same time.

The queen's ability to move in eight directions as many squares as she wants makes her more adept at forking pieces and attacking weaknesses.  Now, if there is nothing to fork or attack, then you're right, the queen is no better than rook + bishop.  Also, if the position is such that the rook and bishop can attack more stuff than the queen, then rook + bishop is actually superior to the queen.  In other words, like most chess platitudes, the real answer is "it depends".  

Even more curious: In positions with two queens vs two rooks + two minor pieces, the player with the two queens is usually inferior, as seen, for example, in Franz-Mayet, Berlin 1858.  The player with the four pieces can generally hold his position together while gradually improving his position, while the player with the queens can't do much to stop this, as queens make poor defenders.  The strength of the queens is their weakness.              

who told you this lies? Rook and bishop are not worth as much asa queen. Not only theoretically seen but also practially the queen is nearly always better. 2 rooks vs queen is a better question, here the 2 rooks are normally better.

In on of the books i've read pretty easy explanation: queen can pretend to be both light and dark-square bishops (switch color by moving like a rook), while bishop can't.

http://danheisman.home.comcast.net/~danheisman/Articles/evaluation_of_material_imbalance.htm

GM Larry Kaufman's detailed statistical analysis of piece value is quite interesting. 

For 2 rooks vs queen, it generally depends on king safety. If they're not stuck defending the king, then the rooks often win by double-attacking pawns, since the queen can only defend it once.

That was the answer I was going to give.   Since you beat me to it I'll throw in a different answer (as ludicrous as the question).   

Because the queen is also a pawn so that adds another point. 

A knight with pawn abilities would be worth far more than 4 points.