Looking at them from the viewpoint of alignment with canon:
MechWarrior 1 aligns fairly closely and references elements from TRO: 3025 and the then brand-new House sourcebooks.
The SNES MechWarrior 1 is a different animal. The developers apparently were working off a copy of Warrior: En Garde for universe setting information, and that's it. So the 'Mechs don't match anything in canon, the main character can get from Galatea to anywhere in the Inner Sphere and back in three days, and the majority of contracts are unlocked by finding holovids left behind in the bar's lost and found bin.
MechWarrior 2 adds extra battles to the Refusal War, but adds some definitely non-canon elements to the fight on Morges, and its linking structure, implying that one Warrior fought in all the campaign's battles and steadily gets promoted from newbie warrior to Khan over the course of the fairly short conflict is lunacy.
MechWarrior 2: GBL has somewhat better alignment with canon, though why the Ghost Bears would have parked their genetic legacies out in the middle of a field somewhere boggles the mind. Also, they accidentally picked a Sword of Light commander from the 3025 Kurita sourcebook, rather than using his successor from the 3050s.
MechWarrior 2: Mercenaries had some issues with canon (like how the unit took Combine missions during the era of Death to Mercenaries), but the recent Shrapnel article cleared that up. Nonetheless, it does turn the brief fight on Wolcott into an extended campaign, and features actions on Luthien that don't quite square with the existing narrative. Overall, though, the journal entries are some of the best writing in the entire series.
MechWarrior 3 seems pretty well tied into the canon events of the storyline, having had its storyline canonized in a BattleCorps serial.
MechWarrior 3: Pirate's Moon seems at least partially aligned with canon, though it can't come too close due to the existence of both an ELH-focused campaign that focuses on fighting the pirates and other factions, and a pirate campaign that takes out the ELH characters pretty early on. Plus, there's that loopy setup for the bonus "final bosses" battle at the end.
MechWarrior 4: Vengeance ties in pretty well with the FedCom Civil War, and there were efforts to reference the Dresaris in novels coming out around that time. However, the FC Civil War sourcebook describes the attack on the Dresari palace as a three day siege, rather than the surprise attack shown in the opening cinematic. Plus, the "good ending" with Ian's sister taking the throne is non-canonical.
MechWarrior 4: Black Knight introduces the fun Black Knight Legion, but doesn't mesh with the official timeline well at all, since Ian (last of House Dresari) retains his position through the duration of the Civil War and his heirs are referenced with pilot cards in the Dark Age.
MechWarrior 4: Mercenaries is great fun, but runs into the issue of the timeline being a choose-your-own-adventure in terms of which missions to take in what order, as well as branching paths. This is further complicated by trying to cram the entire FC Civil War into the last two years (3065-3067), rather than starting in 3063 to align with the canon storyline.
MechWarrior 5: Mercenaries seems to fit well into the storyline, and its prequel novella has been elevated from non-canon tie-in to fully canon source material. The campaign's ending storyline implies that IntelSer did a lot more during its 2980-304X operations than just skulk around the Periphery picking up rumors.