Let's go choice by choice.
Alabama-Mississippi (since 1844)Short-term, this is obviously not the choice to make. However, long-term, it depends. Alabama is already more white than Mississippi, and I recall that the split is slowly growing. I can see this split happening, but only in a total landslide.
Kansas-North Dakota (since 1900)Although North Dakota has more libertarian-leaning farmers, they are still populists at heart, and match Kansas well. This will be a hard bond to break.
Indiana-South Dakota (since 1916)Although they vote similarly, Indiana and South Dakota are fundamentally different states. Indiana is populist, with a conservative Christian tinge, while South Dakota is libertarian, with a Christian conscious. If Dems go libertarian and Reps go populist, a landslide could find South Dakota comfortably in the Dem column, with Indiana comfortably in the Republican column.
Idaho-Utah (since 1916)Beautiful land both (for the most part) and like-minded population (for the most part). Idaho has more libertarians, but the non-Mormons in Utah make up for this by generally being heavily liberal on all issues. These states are perhaps impossible to seperate.
Oklahoma-Virginia (since 1924)Not a very strong bond, although both have fundamentally populist roots. Virginia is trending libertarian thanks to Fairfax and Loudoun Counties, while the rest remains populist. Oklahoma is trending Republican, and socially conservative, while voting less on economic issues than ever. Virginia is much more in reach to the Dems than Oklahoma.
Connecticut-Michigan (since 1944)Michigan may love government to keep its hands off, but it's hardly socially liberal, or even truly libertarian. Connecticut is, for the most part, a socially liberal state. It's also much more Democratic than swing state Michigan. A top pick for a switch.
Colorado-Montana (since 1948)Both states have seen a Democratic surge on the local level, and it would be fair to characterize Montana as Colorado with fewer Hispanics and no big cities. Still, Colorado is much closer - a possible switch, although they should generally trend together.
Ohio-Tennessee (since 1948)A screwed-up economy keeps Ohio very much in play. If it doesn't improve, we're likely to see Ohio go Dem with GOP-trending Tennessee staying in the Republican column. A fairly probable switch.
Illinois-New Jersey (since 1952)Very different states, but remarkably similar voting patterns. Illinois is slightly more solid than the Garden State, but both are within reasonable distance. A careful balance though, since a landslide might take both.
California-Vermont (since 1952)At this point, Vermont seems out of reach for the GOP, so it's a question of whenever California goes Republican next. I'm not betting it will be any time soon.
Hawaii-Rhode Island (since 1960)Pro-incumbent Hawaii could pull off a surprise, but both states have similar views, even if Hawaii is typically much closer. A hard-ish bond to break, although certainly no danger of the GOP taking both states - Rhode Island is a stretch for them in any scenario.
North Carolina-South Carolina (since 1968)North Carolina may be mentioned as more in play, but it's not really by much. Very close states that would be hard to seperate.
I need to sleep, so going quickly through the rest:
Arkansas-Louisiana (since 1968)Arkansas closer. Both states similar. Hard, but in reach enough to be possible.
Delaware-Pennsylvania (since 1972)Pennsylvania on the brink. Delaware not. Very possible.
New York-Wisconsin (since 1972)The Republicans probably won Wisconsin in 2004, but that's a different subject. The easiest possibility.
Oregon-Washington (since 1972)A small landslide could put Oregon into the GOP column but leave more Democratic Washington on the other side of the fence. An unlikely, but possible event.
District of Columbia-Minnesota (since 1976)Whenever Minnesota goes Republican, which could be very soon. Second choice.
Arizona-Florida (since 1980)If Florida doesn't get less GOP in 2008 compared to the national average, these two states could end up voting a lot like eachother. Arizona will always be stronger, though. Both libertarian-leaning. Probable to happen with next Florida flip.
Iowa-New Mexico (since 1992)Rather like-minded states. Too close to sustain, though, but both should remain very close to eachother in voting. Rather likely to split, although only in a close race. Third choice.
My 3 AM "too tired to be doing this, and will regret my idiocy in the morning" rankings are:
1. New York/Wisconsin
2. District of Columbia/Minnesota
3. Iowa/New Mexico
4. Connecticut/Michigan
5. Ohio/Tennessee
6. Delaware/Pennsylvania
7. Arizona/Florida
8. Oregon/Washington
9. Colorado/Montana
10. Hawaii/Rhode Island
11. Oklahoma/Virginia
12. Arkansas/Louisiana
13. Illinois/New Jersey
14. California/Vermont
15. Indiana/South Dakota
16. North Carolina/South Carolina
17. Kansas/North Dakota
18. Alabama/Mississippi
19. Idaho/Utah