Where Did I go wrong?

Well,if you want my opinion,your start was a very nice developing,using nice strategy.White on the other hand,played extremely poorly and using total amateur developing,don't know where to start from.I will only mention that the second move was Qg4??(ouch) and the third Qf4,unbelievable.
But,talking about the part that went wrong,as it is written in the annotations,your move 26.Qxf2 was unacceptable since you had many useful choices.That was not an option at all.Moreover,when you decided to capture the knight by using the rook,27.Rxb7, it was too late and in the worst timing.
Last,it worths to mention that besides your wrong move that it was fatal,i think that if you play with the same player ten times,you won't loose a single game since it requires a lot of time for this player to reach a basic knowledge.
I believe that although you made bad choices and in total your game wasn't good enough,the result was very unfair.

1. d4 d5 2. e3 c6 3. a4 Nd7 4. h4 e5 5. Nc3 e4 6. f3 Ngf6 7. fxe4 dxe4 8. g3 Bb4 9. Qd2 h5 10. Bh3 O-O 11. Bxd7 Bxd7 12. Qe2 Rc8 13. Nh3 a5 14. Nf2 Bg4 15. Qd2 Re8 16. Rf1 g6 17. b3 Nd5 18. Bb2 b6 19. Nxg4 hxg4 20. Rf4 Nxf4 21. exf4 c5 22. Ba3 cxd4 23. Bxb4 axb4 24. Ne2 Rc7 25. Qxb4 d3 26. Nd4 Rxc2 27. Nxc2 dxc2 28. Rc1 Qc7 29. Kd2 Rc8 30. Qxe4 f5 31. Qd3 b5 32. Rxc2 Qxc2+ 33. Qxc2 Rxc2+ 34. Kxc2 bxa4 35. bxa4 Kf8 36. a5 Ke8 37. a6 Kd8 38. a7 Kc8 39. a8=Q+ Kc7 40. Qa7+ Kd6 41. Qb8+ Ke6 42. Qg8+ Kf6 43. Qh8+ Ke6 44. h5 gxh5 45. Qxh5 Kf6 46. Qg5+ Ke6 47. Kd3 Kd5 48. Qxf5+ Kd6 49. Qxg4 Kd5 50. f5 Ke5 51. Qe4+ Kf6 52. g4 Kg5 53. Kd4 Kh4 54. f6 Kg5 55. f7 Kf6 56. f8=Q+ Kg5 57. Qef5+ Kh4 58. Qh8+ Kg3 59. g5 Kg2 60. g6 Kg3 61. g7 Kg2 62. g8=Q# 1-0
another lost game....

When ahead in material, especially by such a large margin, trade down at every opportunity even if it involves giving some of that material back. Like 15./16. Bxb3 would be better as suggested previously. Enough has been said about 26. Qxf2+.

ok, what do you mean by trade down?
When you have more pieces you just trade pieces of equal value: by this I mean eat an enemy knite with your knite or a bishop with your bishop ect.

Here's some analisis for your other game:
After 35. bxa4, your king has no chance to get to where the passed pawn is. An easy way to figure out if your king can cover the distance in time is to draw a diagonal line from where the pawn is to the last row. In this case, that square is e8. Now look at that triangle-shaped territory from e8 to a4. If your king is not in that area, he will never get to the pawn before it promotes.
Just something to keep in mind. You should have resigned at 35.

You should think to start with some piece counting! This may look dumb but even stroong players miss this! its quite simple you count how many pieces attack and hoe many defend X square if you can take it! I think at your level you should play throug games from masters and blitz a lot you seem to be just starting right?

if you are winning by a large margin and they have a rook then take one move to fix back row mating threats. that game was still won after the bishop took the queen.

There are 2 main problems I see with your play, one is easily fixed, the other comes through experience. They are as follows;
1) You missed some obvious things such as, in the 2nd game, the opportunity to pin the Queen to the KIng with the Rook, winning the Queen for the Rook. These things will become more and more obvious as you play more so my advice here is to practice lots on live chess, unrated if you fear for your rating. Practice will also help you blunder less.
2) When your opponent blundered his Queen in the first game, and after you got a Rook for a Knight in the second you were winning in material. In such situation always look to simplify to the endgame by trading off. Remember, when you are up in material, trade off evenly whenever you can, the closer you get to the endgame, with that material advantage still in hand, the more chance you have of winning.
For example, if your opponent goes a minor piece down at the beginning of the game, due to many pawns on the board and the other pieces, through a good move or a pin etc. it is very easy for him to regain the material. However, if you trade off as much as you can after his loss and get to an endgame where you are a whole piece up, you will rarely lose this kind of endgame (provided you don't blunder!!)
Keep up the good work!
I played as black in this game, I thought I had it wrapped up, can anyone explain where I went wrong? Thanks..
1. e4 e5 2. Qg4 Nh6 3. Qf4 exf4 4. Bb5 c6 5. Bc4 d5 6. exd5 cxd5 7. Bb3 Bc5 8. d4 Bxd4 9. Ne2 Be5 10. Nd2 Be6 11. Nc3 Qf6 12. Nf3 O-O 13. Nxe5 Qxe5+ 14. Kd1 d4 15. Na4 Rd8 16. Bd2 Bf5 17. Bb4 Nc6 18. Bd2 Rd7 19. Re1 Qf6 20. Nc5 Rd6 21. Nxb7 d3 22. cxd3 Bxd3 23. Re3 fxe3 24. Bxe3 Rb8 25. Kd2 Ne5 26. Rc1 Qxf2+ 27. Bxf2 Rxb7 28. Rc8+ Rd8 29. Rxd8# 1-0