It is important to ensure the wave extends as far as possible at the State House, Senate, AG, SoS, Gov, Lt.Gov, Mayor, Judge, City Council, School Board, Sheriff and dogcatcher level. Seriously, even at the bottom level Republicans can do a lot of harm. Just imagine cat-killer Bill Frist as your dogcatcher or Sarah Palin on your school board.
In addition to the vital function of building the Democratic bench strength, the State Legislatures and Governorships will be particularly important for the coming redistricting, as the DLCC says:
Time and time again, Republicans have shown that they will cut the Democratic voter base and gerrymander districts in favor of their incumbents, and now, when they take control of a legislature, they aren't even willing to wait until the end of the decade before they go to work.
Currently, of the 36 state legislatures that control Congressional redistricting, 27 chambers in 21 of these states are within 5 seats of tying or changing hands.
These 21 states control 260 Congressional districts.
Here's a table showing some state races to pay attention to:
Office
States Held by Republicans where Obama leading or competitive
States Held by Democrats where McCain Leading
State House
DE, FL, OH, MO, MT, ND, WI
Nil.
State Senate
AZ, FL, GA, IN, MO, NV, NY, PA
MT, WV
State AG*
CO, FL, HI, IN, MI, NH, PA, VA, WA, WI
AZ, GA, KS, KY, LA, MS, OK, TN, WY
State SoS*
CO, FL, IN, MI, WA
AR, OK, TN
* - Ok, I got lazy and didn't go digging to see which of these is actually up for election this year or even separately elected from the Governor at all.
If you live in any of these states and were looking for something to do, I don't doubt there is a local Democratic candidate for State Leg who could use some help (hopefully a progressive). Ohio in particular is really close, especially in the State House.
I didn't forget Governors, there seems to be only two races worth discussing, Washington and North Carolina, where pollster has both Dems narrowly leading. Everything else (it is a light year for Gubernatorial races) is a lock for the incumbent party (Edit: Missouri is a lock to flip R to D h/t to Aaron Veenstra for the correction).
Since Governors have been the most successful at seeking the Presidency, having 29 Democratic Governors to the Republicans' 21 means a significantly stronger bench to draw from for 2016 and beyond.
Also, in the event this Democratic wave leads (eventually) to any constitutional amendments (I can think of a couple I'd like to see), having a big lead in State houses will naturally help grease the wheels.