While I don't know of a generic multi-pitch stripboard equivalent for SMD components, the Schmartboard|ez system and their Schmart Modules, give pretty solid productivity for prototyping, much like stripboard did in the DIP era.
Some examples:

EZ Discrete #1: Supports 0201, 0603, 0805, 1206, 1210, 1608, 1812, 2010, 2512, CAES-A, B, C.

Schmartboard Arduino 206-0007-01: 0.5mm Pitch SOIC Surface Mount Prototyping shield for Arduino
The solder grooves and raised solder resist make it easy to hand-solder small-pitch SMD components, both basic parts like passives, and high pin count ICs. The time saved in DIY prototyping projects is very significant, as well.
The original Schmartboard products were oriented towards soldering an individual SMD IC onto an adapter board, which would then be soldered onto traditional 0.1" pitch layouts. The new module products provide for entire subsystems, i.e. one or more SMD ICs and their associated support components, onto a suitable module, and interconnection of such modules with Schmartboard|ez boards.
Thus, for instance, an SMD RS232 subsystem in its entirety can be prototyped onto a single suitable module board:

The product listing and identification on the Schmartboard site could be a bit confusing, the site could do with some usability reviews and redesign, but the products are excellent.
I have tried similar looking nameless SMD proto boards bought on eBay, but they aren't quite as effective. The Schmartboard grooves, specifically, make a world of difference.
There are specific tools that are designed to cut holes in this material, which is either called "stripboard" or "veroboard". These tools are basically a drill bit in a moulded handle made of plastic or wood and look something like this:

(photo from here)
Because it is basically a drill bit you could use any high speed steel drill bit. There are some good instruction at Instructables that show how to cut neat holes. However if you plan on using stripboard often then it is worth buying a tool with a handle, they are quite inexpensive.
Best Answer
The track of a stripboard is 2mm (78 mil) wide. The holes drilled into them are 0.8mm (31 mil) in diameter, leaving a total (0.6mm [23 mil] on each side of the hole) of 1.2mm (47 mil) for a maximum usable current path. Thickness of Veroboard/Stripboard at 1 ounce per square foot is 35 microns (1.37 mil) thick.
Assuming that you have an ambient of 25 degrees C (77F) and can tolerate of up to 50 degrees C (90F) more, then fed into a pcb track width calculator it spits out:
5.4 Ampere
http://www.desmith.net/NMdS/Electronics/TraceWidth.html