I very rarely do this, but once very very early in my career I actually brought my entire studio to the other side of the country, lock stock and barrel (except the mixing console. Even I have my limits...), and built an ADR-studio in an apartment. That simply will not happen again though.
Nowadays, I see it like this (at least for now); if I really must do dialogue editing in another studio for some reason, I'm just bringing a drive with roomtones and location-based hard effects and foley (you never know), my Nuendo install-disc (all software including ditto Syncrosoft and iLok-keys, of course), my Dolby meter, a few simple dynamic processors and filters (just in case), and two of my main monitors. And a trusty trackball. I hate working with mice or trackpads.
Last time I did sound effects in another studio I brought my complete computer with the then only picture-monitor and patched the DSP Factory-card (impressing at the time. Been very dated for years now) bypassing his console and directly into the patchbay. Now I'd just bring my fieldrecorders, or possibly rent a Cantar, depending on what I'd do.
When doing sound design, on the other hand, things gets a lot more complicated. I try to avoid doing it externally, after all I do have well good stuff myself which I know well (I traded my old Yamaha-cards for state of the art second generation Lynx-cards years ago), but sometimes that's not an option. Things depends on what the studio and the occasion. If I'm just supervising, I just bring my reference headphones and a single large harddrive with all my sound effects. I very rarely do that either though, I like to work hands-on also when supervising. When doing some serious sound designing myself, my luggage would consist of my entire computer setup including all three picture-monitors and Lynx-rig, all five main monitors (right now Yamaha HS80 with phase-corrected bass management, but I'll buy some iNo as soon as I can afford it. The Yamaha's are VERY frustrating to rig...), a switchbox for the listening monitoring (never underestimate the value of some extra reference listening, hopefully already tuned for the room), my headphones, a DVD with all install-files for all my software including Windows (just in case, Murphy's not a lazy man indeed), my location set (K-Tek boom, Fostex FR2 fieldrecorder, different Sennheiser MKH mics, will supplement with linear DPA's, and Beyer 250 headphones, lots of batteries), and a backup harddrive with all sound effects should the internal dedicated effects-drive up and die on me. And of course some reference listening-material on DVD coded in DTS. When I've installed a BluRay in the computer I'll probably change that to reference listening in BD, coded only in lossless. Sounds likely.
But most important of all, I'll make sure I'll have access in one way or another to peanuts/roasted pumpkin seeds, grapefruits/pomelos, and coffee. Some healthy doses of Doctor Pepper is also good for the morale no less, but the caffeine, citrus fruits, and the mineral- and energy-rich peanuts/pumpkin seeds all helps regaining what the brain burns at a ridiculous speed while concentrating heavily for extended periods of time, especially after entering hyper focus and beyond. At my places I have no more than a five minute walk to get that, when in other studios it's a good idea to find out if one can get it anywhere near, of if I'll have to bring it myself.