Bootcamp, Parallels, and Crossover are three completely different approaches to solving the same problem (running Windows apps on a Mac). The first two require a Windows license and install media, while the latter does not.
Bootcamp is just providing the drivers so you can run Windows on the "bare metal" hardware. On the upside, this means your Mac is now just like any other Windows PC in terms of performance and features. The downside is that you can't run any OS X apps at the same time.
Parallels (and VMware) are virtualization environments. They create a "fake" software computer that you then install Windows in, and inside that you can run Windows apps. The upside is that you can still run OS X apps at the same time (since Parallels is just an application). The downside is that performance in some areas (like graphics) is poor, and it uses a lot of memory (since you're running a full blown Windows on top of OS X).
Crossover "pretends" to be Windows. I'm not sure how better to explain it... when you run a Windows app with Crossover, Crossover acts like it is Windows to the application. The upsides are that you can still run OS X apps at the same time, it doesn't use as much memory as Parallels, performance is very good (so you can play your games). The downside is that it is an incomplete implementation of all the possible stuff an application can ask Windows to do; most popular apps (Office, popular games, etc) work, but some don't (they have a list on their website of what works and what doesn't).
For Adobe apps, you'll have native Intel Mac versions soon enough, so I wouldn't worry about them. For 3D apps and games, Bootcamp and Crossover are your only real options, since Parallels just doesn't have the performance for it. Crossover is the "less painful" of the two options, but if it doesn't work for one of your apps, you'll have to go with Bootcamp.
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