What if Sandra Day O'Connor hadn't retired? Let's suppose Bush nominates somebody more controversial than Alito who has to be withdrawn like with Harriet Miers. By that point, O'Connor's husband is too far gone mentally for O'Connor to spend any meaningful time with him and O'Connor decides it would be better to continue serving on the Court.
O'Connor's continued drift left might halt with Roberts on the bench. OTL Breyer was very effective at persuading O'Connor to join narrow opinions and tilt left. Scalia and Thomas irked her in Breyer's direction. But in the six months they served together, she apparently adored John Roberts as another Conservative with a preference for moving the law slowly and ruling narrowly. Whatever effect Roberts has on O'Connor would likely be dampened by Kagan joining the Court though. But Sotomayor might irk O'Connor.
Gonzales v. Carhart (2008) probably goes the same as OTL. The Federal statute was drafted with the Stenberg opinion (including O'Connor's concurrence) in mind.
FEC v. Wisconsin Right to Life, Inc. (2007) probably goes the same as OTL. Five Justices narrowed the McCain-Feingold law, but three (Scalia, Kennedy, and Thomas) wanted to overturn a prior opinion in the process. Roberts didn't, nor did Alito. The Court ultimately overruled that opinion a bit in Citizens United (2010). My guess is Citizens United wins its case in 2010, but with O'Connor as the pivotal vote the decision is a narrower one (probably exempting nonprofits and newspapers entirely from McCain Feingold).
District of Columbia v. Heller (2008) may go the same way too. O'Connor in 2013 chose as a Senior Judge to write an opinion criticizing New York's gun laws as ignoring Heller and McDonald. It might be a much narrower opinion though, since O'Connor just interpreted it as you cannot completely ban guns entirely. She made public statements saying that she thought there was no reason to have an assault rifle.
NFIB v. Sebelius (2012) probably comes out similarly, except there would be a four-justice plurality instead of a three-justice plurality. O'Connor was conservative on federal power and would dislike the Medicaid expansion (she was the only Justice who dissented in South Dakota v Dole on spending clause limits, for example). She publicly seemed to approve of the Roberts position too.
Town of Greece v. Galloway (2014) might go differently.
Whole Women's Health v. Hellerstedt (2016). If O'Connor is still on the Court in 2015, it's possible she narrows the scope of the opinion. Hellerstedt essentially rewrote the Casey Undue Burden test into a benefits-and-burdens test (i.e., do the health benefits outweigh the burdens imposed). Casey just asked if a law amounts to a de facto ban to the women it affected and requires bans on particular sorts of procedures to have health exceptions. The case outcome would probably be the same (Texas's law there would have meant there'd be just one clinic in the state). She might rule more narrowly though (either deal with it as an as-applied challenge, or find that the problematic parts of the law are severable from the non-problematic parts). John Roberts in 2020 OTL basically overturned Hellerstedt by saying the law failed under the old Casey-standard, but voting to strike down an identical law in Louisiana.
EDIT: There's also the issue of res judicata (claim preclusion - ergo you don't get a second bite at the apple in a case). The Hellerstedt majority pretty much sidestepped normal rules on this stuff.
I'm unsure of how O'Connor would rule in U.S. v. Windsor (2013) or Obergefell v. Hodges (2015). O'Connor's Lawrence v. Texas opinion seemed to go out of its way to differentiate laws targeting gay sex from matters like gay people in the military or gay marriage. Perhaps she'd join the majority in Windsor on Federalism grounds (marriage is reserved to the states, and the Federal Government isn't allowed to undermine state definitions of marriage) but a Federalism rationale would cut against her being part of the Obergefell majority.
O'Connor first started becoming forgetful around 2013, reportedly. But she was physically healthy until 2017 (when she began to need to use a wheelchair), but was still able to make public appearances until 2018. Her public announcement of the dementia diagnosis said it had occurred "some time ago." She continued to serve as a Senior Justice sitting by designation
until 2013 though, so I suppose she'd have retired in 2013 or 2014. Or perhaps until 2015, on the assumption that Obama would appoint somebody more moderate if there's a GOP Senate. Harry Reid's proposal OTL to nominate Brian Sandoval might gain traction for the O'Connor seat?