An email exchange with a colleague gave me the idea to post this. So here goes: anything and everything you (reasonably) need related to multimedia (images, movies, audio).
This is probably the simplest, and most expensive recommendation. Photoshop ($999 retail, $299 academic). I don't care what you put Adobe Photoshop against, it is hands down the creme-de-la-creme of image editors. I know, pricey, but you can always get it standalone, without all the other Adobe products. If you're in academia, it is surprisingly 'affordable'. Not only is it good at what it does, but everyone knows what it is, and having mad sk1llZ at PS looks good to everyone. Plus, the number of PS-specific resources online is staggering and if you ever need help or are looking for a particular processing technique, there is probably an online tutorial or plug-in that will make your life easier.
If you refuse to get Photoshop, the most reasonable Open Source alternative is The GIMP (free) or Paint.NET (free). Both are decent and will do 95% or what you probably want. Another less pricey, though not free, option is Photoshop Elements ($199 retail, $69 academic) if you're dealing mostly with photographs. BUT, if you are dealing with nothing but photographs, or take photography semi-seriously, Adobe Lightroom ($299 retail, $99 academic) is an excellent option for organizing and tweaking every setting in regular old JPEGs and RAW images.
For hosting or sharing, either Flickr or Picasa will do the trick. Both have decent free plans, but only Flickr has pro accounts (unlimited storage vs 250MB for Picasa). Avoid Kodak. Avoid it like the F#*&$^#ing plague. Actually, avoid any service that, like Kodak, requires other people to register an account just to view your images.
If you are using XP, I cannot count how many times Image Resizer has come in handy. Right-click an image and select the new size. Bam. Done. XP only, though. For Vista, there's no equivalent. You can try VSO Image Resizer (free), but it isn't as nice. Also, there are some reports of bugs with large batch jobs. There is also this beta app (free), which I have not tried.
First, the basics. Long ago, I got sick of getting video files that wouldn't render because of missing codecs. That's when I found K-Lite Codec Pack and K-Lite Mega Codec Pack (both free). I've been using it for 6 or so years and it has never let me down. It basically bundles all the most current versions of codecs into a single installer. Every 6 months I uninstall it and install the latest version. it also installs Media Player Classic, which is just the old version of Windows Media Player with support for all those codecs. It launches fast, plays smoothly, and just works.
Along the same lines, two video related pieces of software suck on Windows: Quicktime and RealPlayer. Enter Real Alternative and Quicktime Alternative (both free). Bam. No need to install RealPlayer or Quicktime (except when iTunes forces you to).
Okay, now you can see your videos. Yay! Want to convert them to other formats? This is dicey all around. I have tried tens of software solutions and settled on Xilisoft Video Converter ($35). It isn't perfect, but it works 90%+ of the time. You can also try MediaCoder (free), though I haven't had as much luck as with Xilisoft. These are intended for simple/consumer level conversions, not high quality jobs. They're simple, with a minimal learning curve.
For DVD playback, I use WinDVD ($35). It is simple to use, but packed with a billion high quality features if you dig around. It can be a little wonky to set up in Vista, but once you got it, you never have to touch it. The main competitor is PowerDVD ($100), which is more actively supported and has most of the features of WinDVD, but buggier in the past. WinDVD has just bee bought out by Corel, and they are planning an update to v9 'soon' (as of Nov '07). The next time I have to reinstall a system, I will probably switch back to PowerDVD. PowerDVD Ultra will playback Blu-Ray (and HD-DVD) if you have a drive, while WinDVD Platinum's support is shakey.
For all purpose media players, I just stick with Windows Media Player 11. It just seems to work 95% of the time, and isn't an eyesore. But, for those pesky files. there's VLC player (free). There's also a nice portable version for running it off a thumb drive.
Converting between audio formats is much easier. Essentially, there is no reason to use anything other than mp3. It is so widely supported that if a program deals with sound, it will support mp3. While WMP does not support directly converting to mp3, iTunes does (just right click the track). If you want to get more control (MUCH more control) over audio converting, Easy CD-DA Extractor ($32) is by far the best solution I've found. It is the last audio transcoding and ripping program you will ever need. I've been using it for 8+ years. For tagging those files with meta-information, I've been using TagScanner (free). There is a slight learning curve but once you get used to it, again, you'll never use another program. Especially good at batch jobs
For audio authoring, having hosted a podcast, I have found that Adobe Audition ($399 retail, ~$150 academic) is the best, simple program out there. Again, you pay the Adobe premium, but of all the programs I tried (Cakewalk, Vegas, Sound Forge, and a few others) it was the most intuitive and offered the best quality output with the least amount of work. My main concern was noise reduction and cleaning up audio, along with filtering, and Audition delivers in spades.
If you want to go the free route, the gold standard is Audacity. Simple and quick, with a wide user base, Audacity is very good for an OS project, but lacks the fine control and intelligent automation of Audition. When converting to Vista, Adobe was slow to add Vista support, and I ended up using Audacity for several months. I was generally pleased, but had a few instances where the program just quit for no reason after hitting the stop button (which I was oh so happy about after recording a 45 minute show). Also, the 1.3.x version has been in beta forever (at least a couple years).