Should a sequel be judged purely by its own merits, without any regard for prior games in the franchise?
No, never. A sequel is, by definition, a follow-up to a prior work of fiction. Therefore while it should be judged somewhat on its own merits, it is inevitable that it should be compared to its prequel(s). As
laclongquan mentions, many developers don't stop to take a look at what has come before. As a result many developers are re-inventing the wheel, with the appropriate self-pats on the back and exclamations of "Eureka!"
Games should strife to be as faithful to their prequels as possible, the most revered and best game-series made did this (at least on the PC, my limited console experience hinders me from speaking of those platforms) but that doesn't mean that there isn't room for improvement.
Fallout has been mentioned, so let's start there. The original has a clumsy interface, a wonderful turn-based combat system, minimal interaction and control with party members, jokes and "shout-outs" (the modern-day term for pop culture references) that fit and compliment the setting, rather than take the piss out of it, and finally an open-ended world and approach to solving the quests thrown at you. Fallout 2, being a "one-year" sequel (developed in roughly the span of a year) is a very faithful sequel, yet it improves a little on the clumsy interface, makes virtually no changes to the turn-based combat system, greatly improves interaction and control over party members... but suffers a little less open-endedness, but in ways that most people don't even notice. As for the jokes and shout-outs... Fallout 2 tries way too hard in both categories, to the point that until Dungeons of Dredmor came along in 2011, Fallout 2 was the game with THE biggest amount of shout-outs, clocking in at around 400 of them. (I'm not sure that Dredmor even beats Fallout 2, but it's the first game in all these years that even has a chance to do so.)
Another example? Star Control. The original was a mix of a Spacewar!-clone fused with a very simple strategy game, and... that was it. The setting and backstory was cool and thought-out, but it all felt like a weak excuse to get those spaceships fighting one another. There was very little there that looked like it could grow into something more. 2 years later Star Control 2 is released. It retained the core element of the Spacewar! combat, but ditched the simple strategy game completely and went in a whole different direction, an open-ended exploration/adventure game with interesting alien species, a riveting plot and some very memorable gaming moments. The shift is so great that it's almost a reboot of the series and not a sequel. And yet the comparisons will be made, which just goes to show that even in the cases of franchise reboots, comparisons will be made to the originals/prequels. As for Star Control 2? It's not just a cult classic, it's one of the best PC games ever made. It dared to do something drastically different, and succeeded. Very few game series can claim the same.
But the other side of the argument is when a game cannot escape from the shadow of its prequel(s) and receive a fair treatment. Again the Star Control series points this out with Star Control 3. Compared to its prequel, the only innovations present there were technical. More realistic graphics, an attempt to make the game appear to be three-dimensional, full voiceovers. Everything else that was changed or added resulted in an inferior game to its prequel, to say the least. Many Star Control fans simply refuse to acknowledge SC3. I can't blame them. But what if you remove Star Control 2 from the equation entirely? Try to look at SC3 as a standalone game? Then it isn't
that bad a game. It's a fairly enjoyable space opera, and technically it's a Legend Adventure game, those are above average in general, aren't they? SC3 has its share of memorable moments and can be as funny as SC2 at times. As a stand-alone space opera it probably would have fared better. The same argument applies to Fallout 3, if that had just been a generic post-apocalyptic game, we wouldn't be hating on it as much as we do. But it is, and we are. SC3 would have fallen into that limbo state of 90s games that people really don't seem to care about, instead of being vilified and hated by its fanbase.