The suggestion of the "Opera Game" is a good one, but I'm afraid it still might be too advanced for a complete beginner. What might be more suitable would be the elementary games in a beginner's chess manual, of which there are numerous available. These are probably not going to be famous games between well-known players since they would be too sophisticated. If a well-known player would be involved, his opponent would most likely be a novice who would fall into an elementary trap. The following short, instructive game from Ken Whyld's "Learn Chess in A Weekend" did involve one famous player, Paul Keres.
[Title "Caro-Kann, Keres-Arlamowski"]
[FEN ""]
1. e4 c6 2. Nc3 d5 {beginning the fight for the all-important center squares to gain maximum mobility for his pieces} 3. Nf3 {development toward the center in preparation for castling} dxe4 4. Nxe4 {recapturing to maintain material equality} Nf6 {challenging the centralized knight} 5. Qe2?! {defending the knight and setting a trap. This move really isn't the best since it blocks in White's king bishop, but White is hoping for a Black mistake} Nbd7 {Black, seeing only a knight exchange on f6, overlooks that his e-pawn will be pinned to the king if the knight on e4 moves elsewhere and blunders away the game} 6. Nd6# {a "smothered mate"}
The following short game from Savielly Tartakower's "A Breviary of Chess" is between two famous players and is well known.
[Title "Caro-Kann, 1910, Richard Reti-Savielly Tartakower"]
[FEN ""]
1. e4 c6 2. d4 d5 3. Nc3 dxe4 4. Nxe4 Nf6 5. Qd3 {better than in the previous game} e5 {to open lines of play for the pieces} 6. dxe5 Qa5+ 7. Bd2 Qxe5 {regaining the forfeited pawn, although at the cost of several tempi, which are important in the opening when time in development is of the essenc} 8. O-O-O {instead of defending his knight by 8.f3, White conceives a plan to emphasize his lead in development of four pieces in play versus two} Nxe4 {falling into the trap} 9. Qd8+! {sacrificing his queen to force checkmate!} Kxd8 10. Bg5+ {double check, from which the king can only flee} Kc7 {or 10... Ke8 11. Rd8#} 11. Bd8#
Other beginner's manuals will have similar instructive games. Such books by I.A. Horowitz, Fred Reinfeld and Irving Chernev were popular during my older generation, but I'm sure current books for beginners are just as good.