Well TheGeneral brings up valid points. I do feel, that despite Peach's many faults, she dserves to be where she is. Peach can be gimped, as JFox mentioned once you learn out to exploit her weaknesses, but any good player knows their own character's weakness, too. Peach has crazy priority on her aerials and despite how she may match up against...say Fox or Marth, she can still make use of her amazing abilities.
In reality, Peach's worst nightmare is Fox, by far. Reason being is that a smart Fox won't leave any openings for Peach to punish him for. Marth, albeit a small one, does have the advantage over Peach in a matchup. However, a good Peach can make use of her CP, and also her ability to force Marth into approaching her. The matchup seems like a nightmare, at first, but in reality, it's just avoiding the ability to get baited into Marth's juggling. Sheik, although hard at times, can be won out by baiting and punishing. It all comes down, once again, to how smart a Peach plays. Falco, is the most debatable of her matches in the top 4. The reason being, is because most Falco players believe that it's an even match up. It truly is, though. and in some cases, a Peach can have the advantage. Peach can utterly **** a Falco that does not make proper spacing with his Dairs into shine. The lower the better for Falco. Also, Peach's upB OOS, can limit a Falco's ability to apply the shield pressure and approach with his Shine. However, again, if a Peach doesn't play smart, she can fall prey to lasers and shines. Falco can combo Peach pretty well.
Other characters- The part that does get me, however...is how Peach can struggle with lower Tier characters. Y. Link can be a horrid time, as well as Link. Zelda can cut off Peach's turnip game, Bowser can also be a major issue. Again, all can be overcome with smarts.
The top 3 characters shift back and forth because of their ability and priority. However, Falco, like Peach, can be gimped very easily, and earned their spots in the top 5 through development and sheer exploitation of their good points. Peach has plenty of them as mentioned by TheGeneral.
Her ability to FC and DJC give her an edge over what would seem like insurmountable odds towards other characters. FC and turnips give her a nasty edge guarding game. As sadi by Eggm, a fame- perfect Pillar will hold a character in place until a.) the shield breaks, or b.) the Peach player messes up. (lol, I should get AR and start practicing that.) Peach's air game is so dangerous, and a good DI can keep her alive to ridiculous %, against even Fox/Marth. She has the ability to Chaingrab most characters. (Dthrow works wonders on floaties, though if you feel I'm wrong..feel free to correct me.)
Counter Picking- Peach has a good variety of levels for her CP. The strange thing about her is that most people will ban a neutral stage, (usually it's DL64) leaving many other options open for her CP. MOST of the CP stages work to her advantage and a smart CP will win the day for Peach. Mute city is by far the most widely used CP for Peach, and it works well. It limits characters greatly, especially those who like to sweetspot edges. Poke' Floats is another great CP for those annoying Fox/Falco mains. (careful of their secondaries, though) Japes is another amazing CP stage that can work well in Peach's favor. Of course some of the neutral stages work great for CP's aw well but a good use of mixing in those is also part of Peach's game. The ability to CP well with Peach, due to her versatility in styles puts Peach where she is.
Teams- Now I know that JFox didn't mention this, but Peach is also an amazing teams character. She works well with other characters, (herself included) and can switch roles of being an aggressor or stock holder. In a 2 on 1 situation, Peach is solid and does extremely well. Making use of her quick aerials and her Dsmash, peach can turn a game around rather quickly. Her turnips...though potentially harmful to her partner, can easily be one of the greater assets of the team. A good turnip game, and knowing when and when not to use them will make or break a matchup. Peach is also good for helping other partners recover.
Recovery- Peach has one of the best recoveries in the game. She's got a good sense of versatility and because she's so light she can approach high or low with ease. Her second jump and ability to float can make what seems like even the most impossible recoveries possible. True, when you're are reduced to solely the parasol, you can be gimped, but a lot of times those situations can be avoided. She also has her wall bombing technique which can be greatly assisting.
Turnip game- This can make or break a peach, and although a good turnip game can be done without...it's just not good to not have a turnip game. Sastopher made use of Peach's turnips especially in times of needing to win. JFox has a nasty turnip game and uses it to his advantage, especially in Peach dittos. Turnips can throw a person's game off entirely, too. Especially if you have a Stitchface or Bob-omb. A turnip can also, turn a match around with those same two turnips, or even a beady eyes or beam saber. A great peach will have have a good mixup of a technical and turnip game. Peach's turnips are essential to her being where she is in the Tier list.
I don't think I need to mention the Dsmash...it's the most feared weapon in Peach's arsenal. So I'll leave it at that. There are plenty of good things about Peach that puts her where she should be on the list. I'm sure if I missed something...which I probably did, someone else will bring it out. Peach, is in no way as amazing as Fox/Marth/Sheik, but she deserves to be where she is. Despite her many flaws, and the horrid frustration that many, if not all Peach players get when all that hard work is put to shame by a campy fox that sneaks in Drillshine -> Usmash or Uair Uthrow. Lower level Peach players also have issues with overcoming the waveshine happy Foxes that are needlessly aggro.
I know I'm not a great Peach player, but I've seen a lot, studied a lot and have had my own experiences. I hope that some will take what I say seriously...and not just overlook it.