Well, it's a little difficult, but I'll give it a shot.
There's the original, which was first released on NeoGeo in 1996, but got ported to various other platforms, including Saturn, the original PlayStation. Had only two playable characters (Marco and Tarma), determined by whether you were Player 1 (Marco) or 2 (Tarma).
Next came the second game, two years later, which added Eri and Fio, character transformations and additional vehicles and power-ups. This was later remade into Metal Slug X the following year, which appears to be more popular than 2, at least in my experience. Metal Slug X is the game that's coming to Steam next month.
Then there was Metal Slug 3 in 2000, which appears to be one of the most popular games of the series. It was also the last Metal Slug made by the original SNK before they went bankrupt, which is probably why just like KoF 2000, it's among the most popular games in the series. Same 4 characters as 2/X, but it added in branching paths in stages, increasing the game's replay value. This was the game previously released on Steam earlier this year.
Metal Slug 4 came next in 2002, after SNK's bankruptcy. It was developed by Mega Enterprises, a Korean company. This is similar to the cases of KoF 2001 and 2002, which were developed by another Korean company, Eolith. It replaced Tarma and Eri with two new characters, Trevor and Nadia. I'll be honest I didn't play much of this one, but I've heard it's not too popular. It was published by Playmore before they rebranded themselves as "SNK Playmore".
Metal Slug 5 was the last game in the series to be released on the NeoGeo MVS arcade hardware. Noise Factory and the newly-rechristened SNK Playmore took over development on this game. Eri and Tarma came back, and it was generally considered an improvement over 4. Once again, I have very little experience with this one.
Metal Slug 6 came out on Atomiswave (much like KoF NeoWave and XI) in 2006. It added in Ralf Jones and Clark Still from KoF/Ikari Warriors as playable characters and they each had a special move from KoF (Ralf has Vulcan Punch while Clark had his Argentina Back Breaker). Didn't play too much of this one, but what I did play was fun.
Finally, in the main series, there's Metal Slug 7, originally released on the Nintendo DS. This was later remade and upscaled into Metal Slug XX for XBLA and PSP. The main game included the entire MS6 cast, but XX added Leona Heidern (Ralf and Clark's teammate from KoF since 1996) as a DLC character. Never played this one, but I'd love to see XX get ported to Steam.
Then you've got the spinoffs. There were two games on SNK's handheld, the NeoGeo Pocket Color, respectively Metal Slug 1st Mission and 2nd Mission. The games weren't bad given their technical limitations. Metal Slug Advance was a unique game made for the Game Boy Advance (never played it). There was also an exclusive game for the PS2, simply titled "Metal Slug" which turned the game into a 3D shooter. Never played that, but it didn't look so good. There's also a tower defense spinoff on iOS and Android phones called Metal Slug Defense, which recycles a whole lot of graphics from the 2D games. It's pretty fun as far as timewasters go.
tl;dr: There are 7 mainline Metal Slug games, 2 remakes (2 > X, 7 > XX) which are generally considered improvements, 3 spinoffs that played like the main games and 2 others that occupy different genres (3D shooter and tower defense, respectively).