The App Browser lists a whole lot of apps. Here's a few of the most useful for beginners.

FunctionApp nameDescriptionApp Browser name
File ManagerpcmanfmFile manager (explorer)pcmanfm.tcz
Web BrowserOpera browser a basic web browser opera.tcz
Web BrowserFirefoxa full featured web browserfirefox.tcz
Instant Messagingpidginmulti-protocol Instant Messaging (IM) clientpidgin.tcz
Office AppOpen Office word processor, spreadsheet, slideshow, drawing, databaseoo2.tcz
PIMosmoPersonal Info Manager: addressbook, calendar, tasks and notesosmo.tcz
Image EditorgimpGnu image manipulation program (like Photoshop)gimp2.tcz
PaintmtPaintPaint program create bitmap graphicsmtpaint-3.21.tcz
DrawinkscapeliteVector graphics draw program (like Illustrator)inkscapelite.tcz
Music PlayerRhythmboxMusic playerrhythmbox.tcz
Video PlayervlcMedia player plays most audio and video formatsvlc.tcz
Music workstationlmms04Linux Multimedia Studiolmms04.tcz
Email appthunderbirdEmail programthunderbird3.tcz
ClockxonclockAnalog clockxonclock.tcz
CD/DVD burning toolBraseroCD/DVD burning appbrasero.tcz
Plain text editorbeaverA simple text editorbeaver2.tcz
EBook readerfbreaderEbook readerfbreader.tcz

Games

Tetrisitetrisintelligent tetris gameitetris.tcz
Breakoutlbreakouta breakout gamelbreakout.tcz
PinballpinballEmilia Pinball gamepinball.tcz

Full list of currently available apps/extensions for TC: http://distro.ibiblio.org/pub/linux/distributions/tinycorelinux/tcz_2x.html