The best *ever* programs I use(d) are:
For DOS:
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Norton Utilities : NU was
way ahead of its time. It was *the* suite that still makes people miss their good ol' DOS days. My personal favourites were NCD, NDD, NC, DISKEDIT, SPEEDISK and NDIAGS... NDIAGS especially was incredible - one of the tests was an internal PC-speaker test, in which NDIAGS would 'speak' the word "Hello" in 5 different languages! (This was in a time when soundcards were rare and internal speakers could only beep!)
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SpinRite : One of the few DOS programs that I still use today. Simply incredible, the way it used to revive dead floppies and HDDs. Out-of-this-world technology employing flux reversal synthesis. The latest version (v6) is impressive even today - this single 169 KiB exe runs in both Win32 AND DOS as a native app, can create a bootable floppy or ISO image of itself, and works on almost all popular filesystems!
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Cheat Machine : A cheatbook-like program, but way advanced - the whole interface was like a game itself, complete with great sounds, animation and graphics. This was also one of the first programs of its kind. The most interesting feature was that it could directly patch many games so that cheats could be enabled or created! Other specialities included trainers, cheats for other platforms, easter egss for software like norton.. all built with a really cheeky copy-protection. I had opened CM in a hex editor once to try and disable the shareware nags, and I was quite amused when I saw the string "
What the hell are you doing? You're not supposed to be in here!" staring at me in the machine code!
Many years after we all moved onto Win9x, the author of CM decided to give away the DOS version as freeware. I sent him a mail thanking for it and wondered whether he would do the same for the win32 version. He replied "
Does a baker give away his bread for free?"

Unfortunately, that decision ultimately cost him his bread, as no one in the win32 world liked the idea of a shareware cheats database. Cheatbook had arrived. :|
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Arachne : Arachne was a standalone, DOS based, full GUI web browser. It could support both dialup and ethernet, and featured a builtin dialer, telnet, email client, file manager, multimedia viewer and more. The best feature though was that new features could be added by means of downloadable add-ons! One such add-on enabled Arachne to play audio files thru the internal PC speaker for those who didn't have a soundcard! All of this was packed with snazzy skins and themes. It even had loads of screensavers! Oh, and did I mention that the surfing was fast? Maybe even faster than Opera at that time

Back in 1999, my HDD had crashed and I couldn't get a new one immediately. This made me wonder if I could use the PC in this internet age. without a HDD, surviving solely off floppies. Armed with Arachne in one floppy and my custom boot disk in another, it was really a cinch! One program worth mentioning is
QuickView, which could play many popular audio and video files by itself - yes, even DivX files!
For Windows:
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Norton Utilities (for win9x) : I remember this easter egg in one of the NUs - it featured the entire Norton crew dancing to
Darude - Sandstorm 
NU had sucessfully migrated to windows, and programs like WinDoctor, CrashGuard, AntiFreeze, CleanSweep, SpeedStart made win9x quite fast and stable. I even survived the WinME days, thanks to NU. Whaddya know, CrashGuard
actually worked!.
Too bad though that after WinXP was released, most of these features became redundant or inapplicable and NU qickly became what it is today - a bloated PoS.
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Dachshund Software : Dachshund's utilities had actually made games work faster on my PC (by reducing the quality of the textures, etc). It also had the ability to tween between frames and thus made low-framerate games look smoother. "Hare" could actually accelerate applications using its 88-bit kernel to optimize common system instructions. "AntiCrash" was as good as NU's CrashGuard. "Battery Doubler" was a lifesaver for my Laptop. What set this software apart was that it was really tiny, compared to the increasing bloat of NU.
Unfortunately, even this utility suite was killed by WinXP.
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Bleem! : Bleem! was a Sony PlayStation emulator. It was the first of its kind and also the best. Bleem was simply incredible - all the games it was tested with worked *flawlessly*, and the program itself was ridiculously simple to use. Games on Bleem actually looked
better than on the PS, as Bleem could take advantage of the PC's 3D card to render games at higher resolutions - so much so that PS1 games looked better on Bleem than they did even on the PS2! Infact, Bleem was so good that Sony slapped a cease-and-desist on them. >_>
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DOSBox : Because I've yet to finish Dangerous Dave. I get to play all my favourite DOS games in their full SoundBlaster/Color/VGA glory. Back in the day, I didn't have a soundcard or a color monitor. Infact, I was using a monochrome monitor uptill 1998!
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Naviscope : This program hasn't been in development since past 7 years, but works well in XP and still is handy. It's a very useful internet utility to view what's going on behind the scenes when you're loading a webpage. Unlike other programs (Ethereal, etc), Naviscope is a simple floating toolbar. When a site is being loaded, every file that's being downloaded gets a progressbar of its own underneath the toolbar. Clicking on that progressbar stops that file from being downloaded. Very useful when you want to know exactly why a particular site is taking so long to load. Naviscope also has built in Ad-blocking, filtering, prefetching, and could work as a proxy server. There's also a very, very useful HTTP header viewer, which I use often to get direct URLs of videos and to capture form POST data. In Win9x, it could tweak the internet connection too. I used to install Naviscope on every PC I used - even in Internet Cafés. Infact, one café was so pleased with improvements in speed and the utility of Naviscope, that they allowed me to surf for free - for lifetime!
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Ad Muncher : The best program of its kind, in terms of efficiency, performance, features, usability and support. This 488 KB program is written almost entirely in assembly; it's blazing fast, stable and uses very little ram. The coolest thing is that AM can filter *any* internet app seamlessly without any manual intervention. And the name is deceiving - Ad Muncher can do much more than just block ads; you can do all sorts of content filtering, modify pages according to your liking, insert/replace JS and CSS codes and more! It even features a builtin IRC and email client for quick support! Ad Muncher saved many a huge bill in my dialup days, and still does. More importantly, it allows you to view websites that way *you* want to.
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cFosSpeed : Another one-of-a-kind program. It's basically a network driver that performs traffic shaping. For very low ping times while playing online games, superb VoIP quality, surfing smoothly while downloading/torrenting, and much much more. Also works as a handy bandwidth meter. (Try the liquid crystal skin and set the window to click-thru)
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Executor : Win+R (Run) fans will love this one. Kick your outdated Run box aside and try out the incredible Executor! Undoubtedly the *best* Run replacement; it's a must have for power users. I could go on and on about how useful Executor is, but since its freeware, its best that you just try it out for yourself. Trust me on this one.
For my worst programs, I haven't come across any *the* worst program as yet, but are many that I don't like:
Bloated programs like Norton AntiVirus (2000+) and iTunes, codec packs (all), and generally any program that claims to increase your PC's performance by applying a whole bunch of registry "tweaks". Add those so called "Ram Boosters" to that category too. I also dislike poorly written Java apps which are resource hogs. *cough*Azureus*cough*.