You can do that with any sampler, software or hardware. Most samplers are not keyboards, though; typically they are either rackmounts, "groove samplers" (which have mpc-style pads or a step sequencer), or software instruments.
What you should get depends largely on your working methods. I use an Akai S5000 (equipped with a USB expansion) with Ableton Live to do what you're describing, but I'm a hardware junkie. I prefer this setup to a software-based one because I don't like to worry about disk/CPU overloads.
My guess is that the majority of producers making sample-based music triggered from a keyboard are using softsamplers and a midi controller. Of the softsamplers, Kontakt is the most well-known and probably the best. (Gigasampler was the most popular until recently and is probably still quite good.) If you use Live, Ableton Sampler has some nice unique features that are attractive also.
(Note:If you're looking at "warping" speech, then keep in mind that only a few samplers have formant shifting*: the Roland Variphrase sampler was the first one to incorporate it, but it fell off the map quickly after its release. They are quite cheap now secondhand. Variphrase technology is now available in awesome - and awesomely expensive - Roland V-Synth.)
Summarized: if I were you I'd get Kontakt as a plugin for whatever sequencer you're using and control it with a midi controller, *unless* you don't have an awesome computer in which case get a secondhand rack sampler and control it with a midi controller.
*formant-shifting allows you to change the pitch of a sound without the "chipmunk effect."
