I'm looking at ME3 as the best.(I'm taking all DLC into account in my opinions)
ME1 was good, and the weapons systems were easy to break(pair of frictionless and your weapons will never overheat), but the exploration left a great deal to be desired. The tank was frustrating and, while amusing in the story missions, both it and everything else about planetary exploration turned tedious. The inventory system was largely a crap shot of finding 300 useless guns/mods/armor before you found a decent upgrade with everything else getting turned into omnigel for opening locks.
ME2 changed the gun system and revamped the classes, all for the better in my opinion, but dear god, having to grind out resources through scanning got old. Early nods to what you'd done in the first game were nice, as was the improved quest and journal system.
ME3 took everything from 2 and expanded on it. Multiplayer was nice, as was the expanded arsinal you had access to. The story was brought to a nice conclusion when it was all said and done, plus there was payoff for everything you'd done up to that point. The only major complaint I could think of was that they didn't show enough of the major battles.