Alphas have become quite popular during the last year because prices have dropped and Alphas seem to be most promising architecture for the future. But many people often ask "What can I do with an Alpha?"
Very generally speaking you can do anything with an Alpha what you could do with an Intel based PC. But there are some constraints which could knock out an Alpha for some cases.
The Alpha CPU is different from Intels x86 and Pentium systems. It really is! It has nearly nothing in common with them. Therefor software written for Intel based machines does not run on Alphas. The Windows NT port for Alpha has a neat additional package called fx32 which translates Intel to Alpha machinecode on the fly and does an astonishing good job at it. But Linux does not have something like this. At least not exactly like this ;) There is em86 out there which is derived from the x86 emulator bochs. With em86 you can run Linux-Intel binaries on Linux-Alpha. You will need em86 and the Linux-Intel libraries. Em86 will then interpret the x86 machine code and use the x86 libraries. System calls are translated to Linux-Alpha calls. Nice but very slow. If you have a tool which only runs on x86 this might be a solution but for daily work I do not think so.
Conclusion is that you must be aware that the software you are planning to run is either available as an ready to go Alpha port or available as source code so you can port it yourself. In most cases porting software to Alpha is easy, but some cases are not trivial at all. This has mostly to do with the fact that the Alpha is a true 64 bit system and many programmers did not care about those types of machines when they designed their programs.
Nevertheless Alphas are very nice machines. The architecture is a fresh and clean design and not a historically crippled design. Alphas are the fastest desktop machines currently available and seem to hold that place for quite some time. Alphas are especially good at floating point calculations, in some cases floating point can even be feaster than integer!