Chrome OS can't always run the specific application you need, so here are the best alternates.
Traditional application files, like .exe, cannot be installed on a Chrome device. That doesn't mean you can't get any work done, however, simply that you may need a different application to accomplish the task. We've compiled a list below of the most commonly searched applications, and the known alternatives for them.
Skype is a video conferencing application owned by Microsoft. As of now, Microsoft has opted not to release it for Chrome OS, so it is unavailable.
Hangouts is the name of Google's video conferencing and chatting software. The video conferencing feature allows you to hold a private meeting with up to 10 people, or an unlimited amount if you choose to do a live stream (called "Hangouts on Air"). Additionally, you can also use Hangouts for Android or iOS to text-chat with your friends and family for free, with up to 100 people per group conversation.
iTunes is a popular music management application owned by Apple. As of now, Apple has opted not to release it for Chrome OS, so it is unavailable.
Google Play Music is a cloud-based music management solution. There two type types of accounts, a free tier that allows you to upload songs you already own and stream them to any of your devices for free (up to 20,000 tracks), and a paid plan called All Access that runs $9.99/month and gives you unlimited access to their entire streaming library. Both the free and paid version will work on Chrome OS from the web.
uTorrent is a BitTorrent file-sharing application owned by BitTorrent Inc. As of now, BitTorrent Inc. has opted not to release it for Chrome OS, so it is unavailable.
JSTorrent is a Chrome app that allows you to download .torrent files using only your Chrome device. It was developed by a former BitTorrent Inc employee, and while still very basic, is functional.
Put.io is a cloud-based torrenting service, allowing you to upload .torrent files to their servers and let them handle getting the files from other peers. Their service allows offers remote conversion, so you can have them convert your files to be compatible with all devices for streaming later. There is also an Android app with Chromecast support. Monthly plans start at $4.99/month, and Bitcoin is accepted.
Photoshop is an extensive photo manipulation application owned by Adobe. As of now, Adobe has opted not to release it for Chrome OS, so it is unavailable.
Pixlr is a web-based photo editing option owned by AutoDesk, the makers of many powerful software suites (including AutoCAD). The interface is similar to Photoshop, and it doesn't take much time to get used to the slight layout changes. Pixlr is ideal not just for photo editing, but for graphic creation as well.
PicMonkey is a web-based photo editing tool created by some of the same people that created the massively popular tool Picnik (later acquired by Google). It was named a PCMag Top 100 Website of 2013, and is constantly rolling out new features.
Photoshop Express is Adobe's online version of Photoshop. It features a very basic set of tools, but can still be quite powerful when used by a professional. It also receives frequent updates, meaning that it is getting better and more advanced all the time.
Google now owns SnapSeed, a mobile photo editing app with powerful features. Shortly after that purchase, they began rolling its feature set into Google+, bringing those same powerful photo editing features to the desktop. These tools are available completely free to all users of the Google+ platform.
Microsoft Office is a popular office suite featuring a word processor, a spreadsheet application, and presentation software, among other products. As of now, Microsoft has opted not to release it for Chrome OS, but an official version is available on the web.
Google Drive is Google's office suite, featuring Google Docs, Google Spreadsheets, Google Presentations, Google Drawings, Google Forms, and more. It is available free of charge for anyone with a Google Account, and the files can actually sync to your Chrome device for offline access.
Microsoft Office Online is a lightweight version of Microsoft's Office suite available for free to anyone with a Microsoft Account. It works similar to Google Drive in that multiple collaborates can be working on the same file at the same time, and all changes are saved immediately.
We're still actively building this page to include more apps and more alternatives, but in the meantime we highly recommend checking out About Chromebook, a website dedicated to building a database of this information.