State Legislation Passed
For timeline of passed legislation below and links to the legislative text, see:
U.S. Online Poker & Gaming Legislation History

Legalization:
DELAWARE
Internet lottery, video lottery, keno, bingo and table games (including poker).
Operated by DE Lottery and video lottery agents (i.e., the three DE casinos) on the lottery-run platform provided by 888 Holdings (888.com poker software).
21+ (except 18+ for Internet lottery tickets)
Intrastate: anyone located in DE can play.
Interstate: authorized under interstate compacts.* Currently networked with 888poker in NV.
International: not specifically authorized but possible.
Operational: October 31, 2013

NEW JERSEY
All Internet gaming, including poker.
Sites operated by Atlantic City casinos, with licensing approval for service provider partners:

Sites available at soft launch:
Borgata / bwin.party (PartyPoker) via http://www.theborgata.com/forms/online-games/sign-up or http://poker.theborgata.com/download.html and http://nj.partypoker.com/ (shared player pool)
Caesar’s/ 888 Holdings (888Poker) via www.wsop.com and www.888poker.com (not shared player pool)
Tropicana / Gamesys via https://www.tropicanacasino.com/ (poker expected in Q1 2014 on proprietary software)
Trump Plaza / Betfair (Ongame) via www.letsplaynj.com (poker now closed)
Trump Taj Mahal / Ultimate Gaming (UltimatePoker) via www.ucasino.com (closed in Nov. 2014 due to financial losses)
Golden Nugget / Amaya and Bally Technology (Ongame) via www.goldennuggetpoker.com (shared player pool with Trump Plaza/Betfair) (poker now closed)

Sites not available at soft launch:
Resorts / Rational Entertainment (Full Tilt Poker and/or Pokerstars - approved by regulators on 10/2/15)

AC casinos that haven't yet applied for an Internet gaming permit:
Revel (in bankruptcy)
Atlantic Club (no longer exists)

21+
Intrastate: anyone located in NJ can play.
Interstate: authorized under reciprocal agreements negotiated by Governor with other states.
International: authorized under reciprocal agreements negotiated by Governor with other jurisdictions.* Such an agreement was agreed to between NJ and the UK. However, implementation turned out to be impossible as NJ law requires the gaming servers to be located in NJ, a business model that the Internet sites were unwilling to adopt.
First sites operational: soft launch on Nov 21, 2013; go-live on Nov 26, 2013 intrastate.

NEVADA
Internet Poker only
Operated by NV casinos with licensed service provider platforms.
21+
Intrastate: anyone located in NV can play.
Interstate: authorizes Governor to negotiate agreements with other states.
International: no language that specifically authorizes or forbids it.
First sites operational: UltimatePoker became first site operational for real-money play intrastate on April 30, 2013 (closed in Nov. 2014 due to financial losses); WSOP.com (2013); Real Gaming (2014).
Note: Includes bad-actors provision which excludes for 5 years from licensing any person or entity (or use of their resources) which operated online gambling/poker for US players after December 31, 2006.

PENNSYLVANIA
All Internet gaming, including poker.
Operated by PA casinos with licensed service provider platforms.
21+
Intrastate: anyone located in PA can play.
Interstate: authorizes Governor to negotiate agreements with other states.
International: authorizes Governor to negotiate agreements with other jurisdictions.

U.S. Virgin Islands
All Internet gambling.

Prohibition: FL, UT, WA

Other States That Were or Are Considering Legislation
Legalization:
CA
CO
DC (legislation passed but repealed)
FL
GA
HI
IA
IL
MA
MI
MS
NY
TX
WA (2nd thread)
CT, KY, LA, MD, ME, NH, OH

A page at the National Conference of State Legislatures with state legislation summaries and links:
2015 Legislation Regarding Internet Gambling and Lotteries (hasn't been updated since 2015)