In a pinch, you could look through the multitasking bar that appears when you double-click the home button. The apps are arranged in order of most recently used. It is not a measure of how frequently an app is used, but it could at least tell you if it was used recently, or if other apps have been of more interest lately.

(please contribute to the list with any other apps, and feel free to edit to make the list more accurate--this is a community wiki answer)

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Notation for the list below:

1. With few exceptions, any app falls into on of these categories:

   • it supports System Settings > Dynamic Type and Bold Text (I mark it as "Dynamic&Bold" below)
   • OR also supports System Settings > Larger Text (I mark as "Larger Text")
   • OR has its own app-specific font size settings ("App settings")
   • OR has NO font size customization whatsoever ("No customization")

2. For each app, I also specify how its maximum text size compares to standard system apps at maximum Dynamic Type setting if different (the app font is Smaller or Larger than in system apps)--to make it easier for a given app to understand its text size limit, given only few minutes with built-in apps only at Apple outlet.

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Social networks

Facebook:
- all UGC (News Feed, User Timeline, Individual post and comments): Dynamic&Bold (since 2015-Nov-06); much Smaller
- app interfaces: No customization; smaller

Twitter:
- timeline: App settings (3 sizes); smaller
- settings screen: Dynamic&Bold

Google+: No customization; Much smaller

Instagram: No customization; Much smaller

VKontakte (both iPad- and iPhone apps): No customization; Smaller

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Email apps

Mail:
- plaintext emails: Dynamic&Bold
- HTML emails: font scales only with Larger Text, but not with Dynamic Type(!); but can be much smaller than for plain text emails / than in other apps

GMail: No customization; Smaller (both for plaintext and HTML emails)

Google Inbox: No customization; Smaller (both for plaintext and HTML emails)

AirMail: Dynamic Text, App Settings; no LargerText support (text gets smaller instead)

Calendar (by Apple): Dynamic&Bold

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Task managers

OmniFocus:
- Dynamic&Bold throughout the app
- LargerText for leaf-level outline items and Note editing only; No for outline groups

Things: No customization; smaller

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Instant Messengers

Messages (iMessage):
- history of chat with a contact: LargerText
- list of contacts on left sidebar: Dynamic&Bold

Skype: No customization; Much Smaller

Telegram:
- history of chat with a contact: Dynamic Type (no Bold Text); smaller
- list of chats: No customization; Smaller

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Web browsers

Safari:
- regular browsing: No customizaion; pinch to zoom leads to horizontal scrolling. Smaller.
- has a special Reader Mode with App Settings: wide range of sizes, comparable to the range of Larger Text. Works only for article-type web pages, not everywhere.

All other browsers tried (Google Chrome, Opera, Yandex Browser, iCabMobile): No Customization; pinch to zoom leads to horizontal scrolling. Smaller.

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Office documents

Google Drive: No Customization

Google Docs: No customization: only document zoom, leads to horizontal scrolling. Smaller

Google Sheets: No Customization: only document zoom, leads to horizontal scrolling. Smaller

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Maps

Google Maps: No customization; Smaller

Apple Maps: Dynamic Type only

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Other built-in apps

Settings: Dynamic&Bold

Notes: LargerText

Reminders: LargerText

home screen: No customization

built-in keyboard: Bold Text only

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Other third-party apps

Pocket:
- list of articles: Dynamic&Bold
- aricle body: App settings: wide range of sizes, comparable to the range of Larger Text

Google Keep: No Customization. Much Smaller.