This summer I've stuck to what I have come to believe is the near perfect build for my Surly. Sure there are always improvements (always always always), but I think this is as close as I've gotten to a bike that handles just about everything I throw at it well. The dirt drops have given me much better control while not compromising grip positions. The wide slickish tires give me good traction off road without slowing me down on the pavement. The wide gear range allows me to go up and down a whole bunch. So what are the key components to building a Monster-Cross bike?
Arguably, you can probably get away with building a Monster Cross bike out of a 29er, by adding dirt drops, but where is the fun in that? Half the fun of a Monster Cross bike is the cross geometries can allow you to get real aggressive on the paved stuff. The key thing to look for in finding your monster cross build is wide tire clearance and it seems most non-racey bike manufacturers are making that a standard on cross bikes. Some great cross options would be the obvious Surly Cross Check, where people have fit 50mm slicks in there, but there is also the All-City line (single speed Nature Boy, disc compatible or rim compatible Macho Man), or the Soma Double Cross (again disc and rim brake compatibility). If you've got cash burning a whole in your pocket there are some other non-production bikes to look at, my personal favorite built up in Sonoma County would be the Black Mountain Cycles Monster Cross, where you can fit a whopping 29x1.75 (as the name implies these were meant for fat tires), the Rivendell Atlantis can be built up to Monster Cross as well. Notice something about the frame materials on all these? Steel. Carbon and aluminum break much easier, steel will help you tackle those drops not meant for a cross bike.
Before I get too far into tires, one upgrade from a stock bike that will greatly help a monster cross build is wider rims. Wider rims allow for lower pressure and more contact, meaning more cushion and more grip (this is why Monster Cross bikes are better than regular 32 or 35 mm cross options). I have not made this upgrade quite yet but I am looking at the Pacenti PL23 and the Velocity A23 rims, both 23mm wide, which I think is a great size for a Monster Cross bike, but for those daring enough you can go as wide as 35mm as road racers have taught us about 23mm rims with 23mm tires (also tubeless is your friend for the same reason).
Now, tires. In my opinion, slick and wide is better than narrow and knobby. You can fit a wider slick tire for the fact that the knobs don't protrude out. I particularly like this too because it makes road riding much better. I have been running the Marathon Mondials in a size 40 (I want to upgrade to the 29 x 1.75 when I upgrade rim size). They have been a dream. Only sometimes in the mud, steep inclines, or sand do I feel my tires give out, but the side profile I think helps with that to some extent. As wide tires are gaining popularity there are many options out there, some 'tweener tires I like would be the Kenda Happy Medium, the Ritchey Speedmax tires, and Surly has unveiled their own 700x41 version of the Knard.
I wrote recently about the On-One Midge bars. Dirt drops I feel are really important to riding a cross bike off road, as cross bars aren't really meant for gnarly descending (although I have seen some much better riders than me knock out crazy descents on slightly flared cross-bars). A quick run down on dirt drop options would the On-One Midge, Soma Junebug, Salsa Woodchipper, Origin-8 Gary bar, or the vintage Specialized BB-2.
Touring, day riding, off-roading, road-riding, a Monster cross bike I feel is the perfect do-it all bike. Of course I blabber on and on about Monster Crossing, but it truly has been great to conquer off road segments on a traditional diamond frame, of which no Mountain bike manufacturer makes anymore (except Rivendell, go Riv), accommodating for suspension. Sure your cross bike is not going to conquer park, or real rocky sections, but it's a cross bike and is therefore meant to be carried too. The best part is though, a 30 mile ride to a trail head won't wear you out as much as a full suspension mountain bike would.