Making fonts larger in apps under Lion

Solution 1:

Safari

For Single Page

Press ⌘ + to increase text size on the page.
Swipe in or double-tap with two fingers to zoom into a page (iOS-like).

Note that text zooming and page zooming are not quite compatible and may cause odd effects when combined so you should stick with either.

For All Pages

To make Safari “remember” your text zoom setting, use a custom stylesheet:

1) Create a file named defaultzoom.css (or any name you like, just make sure it has a css extension.)

2) Copy and paste in the following:
    body {  
      zoom: 130%;  
    }
change 130 to whatever number suits you. >100 means zoom in, <100 means zoom out. Don't forget the % percent sign!

3) In safari, go to Preferences > Advanced. Under style sheet, select Other... and point to the file you created.

4) You may need to restart safari for the change to take effect.

For Certain Websites

Personally, I prefer keeping text zoom level per site with ZoomBySite extension by Ceri Morgan.
It overrides the keyboard shortcuts and remembers the last text zoom level for domain.

Solution 2:

Google Chrome

Its own UI, not web pages

The following settings in TinkerTool affect the following pieces of Chrome's own UI:

Chrome address bar, i.e. URL: System in TinkerTool (default font: Lucida Grande; largest size possible is 16 pt; larger sizes are truncated)
titles of tabs: Help tags (default font: Lucida Grande; largest size possible is 13 pt; larger sizes are truncated. Bold is ignored, it's always Regular)
Chrome's ex-Wrench menu (top right corner): Messages (default font: Lucida Grande; upper limit is something like 24 pt, further increasing the number has no effect)

Web page content

Default zoom: Wrench > Settings (⌘ ,) > Show advanced settings > Web content > {Font size, Page zoom}. Both also affect how Settings page is zoomed.
For a particular site: ⌘ + / ⌘ -