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The S3a/c/mx A-List
Games
Slick and addictive, there's no better way to pass the time!
De3ender
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Lightning fast and faithful to the generation-shaping original coin-op. Will have you cursing and cheering in equal amounts as you fight off the evil aliens trying to steal your humanoid team. Available from Mark Wheadon.
Alternatively:

Scrabble
Polished commercial strategy game, with wonderfully customisable views of the board and challenging gameplay.

Fairway
[Ahem] Yes, this is one of mine, but I make no apologies as this is perennially popular. A complete 3-D golf simulation for 1 or 2 players. Available on the original Psion 3a Games Pack or as shareware.

Business software
Worthwhile add-ons to the built-in Psion application set
PsiTact Lite
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Intuitive contact manager, with Data, Word, Sheet and Agenda integration. Good search and reminder functions make the program invaluable to the businessman on the move. See Tony Crocker's web site.
Alternatively:

Plan
Legendary in the Psion world and as powerful as many desktop project planning packages. Manage your resources and timescales in any of the different views. See Twiddlebit for details.

Facilities Manager
A versatile management tool to track usage of any resource, whether personnel or material. See Gary Bainbridge's web site for details.

Database software
Extra functionality beyond that of the built-in Psion DATA application
JBDATA
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The all-time most popular 16-bit Psion program and deservedly so. Whether you're looking to sort, search, list or hack, this database tool can do it all. It may be slightly idiosyncratic in operation, but it's very fast and at a price point of being err... absolutely free(!) you can't really go wrong. See John Boyce's web site.
Alternatively:

DataView Pro
Think of this as JBDATA with a prettier interface and some nifty printing routines. Polished commercial software, with excellent support for those Christmas mailing labels! See Handango for more details.

3Base
An ex-commercial product that's now been made freeware (download here), this is a PC/Windows application that does every kind of .DBF (DATA) conversion you could ever imagine. Again a rather quirky interface, but then it seems to come with the territory!

Utilities
Small but useful widgets than no Psion owner should be without
JBFind
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It's almost tempting to just call this category "John Boyce's programs" as he's written so many good little freebie utilities... This is one of the most popular. JBFind searches all drives and inside files looking for text strings of your choice. If you've ever named a document erroneously and subsequently lost it, this utility is invaluable and worth hanging on your Psion 3a/c/mx's virtual Swiss Army Knife... See John Boyce's web site.
Alternatively:

JBActive
Yes, it's Mr. Boyce again! JBActive is the ultimate control utility for Psion power users. It allows fast switching and launching of programs, plus full backlight automation and system information screens. See John Boyce's web site.

JWIN
Standing for "Just What I Need", this shareware utility aims to combine a wealth of unit conversions, system information screens and more off-the-wall calculations. Judging from the registration counts, it appears to have succeeded. See Phil Spencer's web site.

Graphics software
Making the most of the Series 3a/c's graphics capabilities
Draw
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Ahem. Please don't think my top recommendation is at all boastful, because it's not. Draw was written by Rick Andrews and 98% of the code is entirely his. I've only recently taken over management of the program (because he now has other commitments) and the only reason I agreed to do this was because I've been a fan of Draw for 4 years now. With real-time zoom, area-filling and pattern management, it really is the last word in 16-bit Psion painting software and it takes the genre as far as humanly possible given that the Psion doesn't have a mouse! See the Draw home page.
Alternatively:

Vector
Programmed in highly-optimised C, this is a powerful CAD-like vector graphics program with drawing layers, multiple zoom levels and object selection. See Nick Matthews' web site for more details.

DrawIt
Another vector drawing program, which used to be commercial but which I've been given permission to distribute here, with several polished features including good printing support and good text-box handling for pseudo-DTP work. Download here as drawit.zip.