method to describe all fontName in iOS 7, ordered alphabetically. Also: all the fonts found in 7.0.3.

describeAllFonts

+ (void)describeAllFonts
{
    NSMutableArray *fonts = [NSMutableArray array];
    NSArray *familyNames = [UIFont familyNames];
    for (NSString *familyName in familyNames)
    {
        NSArray *fontNames = [UIFont fontNamesForFamilyName:familyName];
        for (NSString *fontName in fontNames)
        {
            UIFont *font = [UIFont fontWithName:fontName size:14];
            [fonts addObject:font];
        }
    }

    NSSortDescriptor *sort = [NSSortDescriptor sortDescriptorWithKey:@"fontName" ascending:YES];
    fonts = [fonts sortedArrayUsingDescriptors:[NSArray arrayWithObject:sort]];

    for (UIFont *font in fonts)
    {
        NSLog(@"%@", font.fontName);
    }
}
/*
 AcademyEngravedLetPlain
 AlNile
 AlNile-Bold
 AmericanTypewriter
 AmericanTypewriter-Bold
 AmericanTypewriter-Condensed
 AmericanTypewriter-CondensedBold
 AmericanTypewriter-CondensedLight
 AmericanTypewriter-Light
 AppleColorEmoji
 AppleSDGothicNeo-Bold
 AppleSDGothicNeo-Light
 AppleSDGothicNeo-Medium
 AppleSDGothicNeo-Regular
 AppleSDGothicNeo-SemiBold
 AppleSDGothicNeo-Thin
 Arial-BoldItalicMT
 Arial-BoldMT
 Arial-ItalicMT
 ArialHebrew
 ArialHebrew-Bold
 ArialHebrew-Light
 ArialMT
 ArialRoundedMTBold
 Avenir-Black
 Avenir-BlackOblique
 Avenir-Book
 Avenir-BookOblique
 Avenir-Heavy
 Avenir-HeavyOblique
 Avenir-Light
 Avenir-LightOblique
 Avenir-Medium
 Avenir-MediumOblique
 Avenir-Oblique
 Avenir-Roman
 AvenirNext-Bold
 AvenirNext-BoldItalic
 AvenirNext-DemiBold
 AvenirNext-DemiBoldItalic
 AvenirNext-Heavy
 AvenirNext-HeavyItalic
 AvenirNext-Italic
 AvenirNext-Medium
 AvenirNext-MediumItalic
 AvenirNext-Regular
 AvenirNext-UltraLight
 AvenirNext-UltraLightItalic
 AvenirNextCondensed-Bold
 AvenirNextCondensed-BoldItalic
 AvenirNextCondensed-DemiBold
 AvenirNextCondensed-DemiBoldItalic
 AvenirNextCondensed-Heavy
 AvenirNextCondensed-HeavyItalic
 AvenirNextCondensed-Italic
 AvenirNextCondensed-Medium
 AvenirNextCondensed-MediumItalic
 AvenirNextCondensed-Regular
 AvenirNextCondensed-UltraLight
 AvenirNextCondensed-UltraLightItalic
 BanglaSangamMN
 BanglaSangamMN-Bold
 Baskerville
 Baskerville-Bold
 Baskerville-BoldItalic
 Baskerville-Italic
 Baskerville-SemiBold
 Baskerville-SemiBoldItalic
 BodoniOrnamentsITCTT
 BodoniSvtyTwoITCTT-Bold
 BodoniSvtyTwoITCTT-Book
 BodoniSvtyTwoITCTT-BookIta
 BodoniSvtyTwoOSITCTT-Bold
 BodoniSvtyTwoOSITCTT-Book
 BodoniSvtyTwoOSITCTT-BookIt
 BodoniSvtyTwoSCITCTT-Book
 BradleyHandITCTT-Bold
 ChalkboardSE-Bold
 ChalkboardSE-Light
 ChalkboardSE-Regular
 Chalkduster
 Cochin
 Cochin-Bold
 Cochin-BoldItalic
 Cochin-Italic
 Copperplate
 Copperplate-Bold
 Copperplate-Light
 Courier
 Courier-Bold
 Courier-BoldOblique
 Courier-Oblique
 CourierNewPS-BoldItalicMT
 CourierNewPS-BoldMT
 CourierNewPS-ItalicMT
 CourierNewPSMT
 Damascus
 DamascusBold
 DamascusMedium
 DamascusSemiBold
 DevanagariSangamMN
 DevanagariSangamMN-Bold
 Didot
 Didot-Bold
 Didot-Italic
 DINAlternate-Bold
 DINCondensed-Bold
 DiwanMishafi
 EuphemiaUCAS
 EuphemiaUCAS-Bold
 EuphemiaUCAS-Italic
 Farah
 Futura-CondensedExtraBold
 Futura-CondensedMedium
 Futura-Medium
 Futura-MediumItalic
 GeezaPro
 GeezaPro-Bold
 GeezaPro-Light
 Georgia
 Georgia-Bold
 Georgia-BoldItalic
 Georgia-Italic
 GillSans
 GillSans-Bold
 GillSans-BoldItalic
 GillSans-Italic
 GillSans-Light
 GillSans-LightItalic
 GujaratiSangamMN
 GujaratiSangamMN-Bold
 GurmukhiMN
 GurmukhiMN-Bold
 Helvetica
 Helvetica-Bold
 Helvetica-BoldOblique
 Helvetica-Light
 Helvetica-LightOblique
 Helvetica-Oblique
 HelveticaNeue
 HelveticaNeue-Bold
 HelveticaNeue-BoldItalic
 HelveticaNeue-CondensedBlack
 HelveticaNeue-CondensedBold
 HelveticaNeue-Light
 HelveticaNeue-LightItalic
 HelveticaNeue-Medium
 HelveticaNeue-MediumItalic
 HelveticaNeue-Thin
 HelveticaNeue-ThinItalic
 HelveticaNeue-UltraLight
 HelveticaNeue-UltraLightItalic
 HiraKakuProN-W3
 HiraKakuProN-W6
 HiraMinProN-W3
 HiraMinProN-W6
 HoeflerText-Black
 HoeflerText-BlackItalic
 HoeflerText-Italic
 HoeflerText-Regular
 IowanOldStyle-Bold
 IowanOldStyle-BoldItalic
 IowanOldStyle-Italic
 IowanOldStyle-Roman
 Kailasa
 Kailasa-Bold
 KannadaSangamMN
 KannadaSangamMN-Bold
 MalayalamSangamMN
 MalayalamSangamMN-Bold
 Marion-Bold
 Marion-Italic
 Marion-Regular
 MarkerFelt-Thin
 MarkerFelt-Wide
 Menlo-Bold
 Menlo-BoldItalic
 Menlo-Italic
 Menlo-Regular
 Noteworthy-Bold
 Noteworthy-Light
 Optima-Bold
 Optima-BoldItalic
 Optima-ExtraBlack
 Optima-Italic
 Optima-Regular
 OriyaSangamMN
 OriyaSangamMN-Bold
 Palatino-Bold
 Palatino-BoldItalic
 Palatino-Italic
 Palatino-Roman
 Papyrus
 Papyrus-Condensed
 PartyLetPlain
 SavoyeLetPlain
 SinhalaSangamMN
 SinhalaSangamMN-Bold
 SnellRoundhand
 SnellRoundhand-Black
 SnellRoundhand-Bold
 STHeitiSC-Light
 STHeitiSC-Medium
 STHeitiTC-Light
 STHeitiTC-Medium
 Superclarendon-Black
 Superclarendon-BlackItalic
 Superclarendon-Bold
 Superclarendon-BoldItalic
 Superclarendon-Italic
 Superclarendon-Light
 Superclarendon-LightItalic
 Superclarendon-Regular
 Symbol
 TamilSangamMN
 TamilSangamMN-Bold
 TeluguSangamMN
 TeluguSangamMN-Bold
 Thonburi
 Thonburi-Bold
 Thonburi-Light
 TimesNewRomanPS-BoldItalicMT
 TimesNewRomanPS-BoldMT
 TimesNewRomanPS-ItalicMT
 TimesNewRomanPSMT
 Trebuchet-BoldItalic
 TrebuchetMS
 TrebuchetMS-Bold
 TrebuchetMS-Italic
 Verdana
 Verdana-Bold
 Verdana-BoldItalic
 Verdana-Italic
 ZapfDingbatsITC
 Zapfino
 */