We're going to use the term "passthrough device" to describe any device that tricks the DS into launching from slot-2 in DS mode, which is normally not allowed by the DS firmware.
The first passthrough device was the PassMe. It required an original game cartridge that could supply the necessary initialization codes to the DS before redirecting code execution to slot-2. Then came Wifime, which merely acted as a wireless PassMe using the Download Play functionality of the DS combined with certain brands of wireless cards for the PC. The DS would download a modified Super Mario 64 DS Download Play image which would then redirect code execution to slot-2. Both the PassMe and WifiMe stopped working after DS firmware 3.
After firmware 4 came out, the PassMe2 was developed which had to be programmed for an exact game you had and required your slot-2 device to have SRAM (locking out the most popular device at the time, the GBA Movie Player). This, like the PassMe, stuck out quite a bit from the DS and was cumbersome to use.
Then came the NoPass, which greatly simplified the process. NoPass devices are the size of regular DS game cartridges and don't require anything else to work. Pop in the NoPass, boot the DS, and it automatically boots your slot-2 device in DS mode. There are several varieties of NoPass devices, including the Superkey, PassCard 3, Max Media Launcher, and even the Action Replay DS if you hold Select upon bootup. See
http://wiki.pocketheaven.com/NoPass for some more brands.
Throughout this entire time, there was FlashMe. FlashMe is a replacement firmware for the DS that you can install if you'd like. The main advantage is that once installed, you no longer need a passthrough device to boot a slot-2 device in DS mode. However, it is a slightly risky process, so you should do some research into the installation if you plan to do it. The main caveat is that you must be able to boot your slot-2 device in DS mode at least once in order to install FlashMe in the first place. In my case, I bought my Superkey for $20, used it once to install FlashMe, then set it aside. The only time I ever use it now is for flashing my friends' DS systems (they like it since FlashMe also removes the Health and Safety warning screen).
Most slot-1 devices nowadays (R4, Supercard DS, DSTT, CycloDS Evolution, etc) contain built-in NoPass functionality that you can use if you need to. So you can either play $20 for a NoPass or spend a little bit extra and get a full-fledged slot-1 device that would expand your game-playing capability plus act as a NoPass on the side. The choice is yours.