Mixing/mastering: I like protools. I think protools and the digi rack is the most intuitive and efficient hardware/software combo for producing final mixes, and/or recording live instruments and vocals.
Mashups: Well, Acid Pro is popular in the dance/electronic crowd. You can record live "performances" of riding fx, eq, pans, etc. You can also create markers in order to fade a particular track in and out over the course of a composition. I suppose you could do the majority of that with Pro Tools, but Acid is easier to pick up and I find it much easier to rip samples, create beats and measures with said samples, and what not.
Creating original beats: Analog equipment is better. Sampler/drum machine combo hardware like the MPC, keyboards, synths, etc. Programs like Reason are fun to play with, but I'm never satisfied with the sound. It is nice to be able to individually track drums from hi hats, to kicks, to snares. Of course, you can buy/download sample packs for all of these programs (incl. pro tools) that would contain both drum "single hits" and full loops. You can integrate Reason into Pro Tools, a definite plus. Other people swear by Fruity Loops, but I've never used it/seen it.