Instant switch weapons?... Nah
Overview -- Currently the time it takes to switch weapons in Quake 3 is 600ms, which is faster than Quake 2, but obviously a lot slower than the instant-switch in Quake. What people don't realize is that Quake's instant-switch weapons were a result from the lack of time to create weapon animations, rather than an intentional gameplay decision by id. After some discussion with the id guys, it became apparent that there would be no plans in implementing instant-weapon switch. Some of the reasons given were that instant-switch wasn't very realistic, it didn't look very good, and it was never a planned feature. (Look at Doom, its weapon switch is even slower than Quake 2)
My Thoughts - I tend to favor changes that promote faster gameplay, and certainly faster weapon switching is one of them. At the same time, I don't think having instant-switch weapons is necessary to achieve that goal. Quake 2 brought a new facet to the game that was not evident in the original - the necessity to know what weapons to use in which situations, and more precisely, before, during, and after battle.
An important note people have not mentioned is that weapon reload times will also play a big role in how quickly a weapon can be switched. In Quake, all weapons fired instantly and none had a very significant reload time. However, in Quake 2 and consequently Quake 3, many weapons have varying reload times, which would make instant-weapon switching awkward, especially for newbies in that some weapons would switch faster than others.
Suggestions to id - The 600ms weapon switch time currently implemented in Quake 3 is just fine, though speeding it up by any amount would certainly be welcomed (especially by Quake players).