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I-130 (future) Arkansas
Interstate 130 will be the official designation for the 5.8-mile Loop 245 in Texarkana from I-30 to US 71, when the highway is completed. The route will be signed "Future I-130" until work is complete. 
Arkansas had requested the designation extending to the Texas state line, but on Dec. 8, 2000 AASHTO approved I-130 only between I-30 and US 71. The reasoning: Route 245 south of there was not a part of the interstate system, and Texas did not submit a companion application for an appropriate terminus in that state. 
12.93 miles ; bypasses Little Rock to the west, connecting I-30 and I-40. Finished in late 1970s.
46.65 miles  Interstate 530 is the new number for a stretch of US 65 between Little Rock and Pine Bluff, from I-30 and I-440 to the end of the Pine Bluff bypass. The "Future I-530" number was approved by AASHTO on Nov. 14, 1997.  I-530 was officially designated on August 2, 1999 when the final segment of the bypass was complete. 
Harder, Better, Faster, Souther
Arkansas plans to extend I-530 about 38 miles south to proposed Interstate 69, at a point between Wilmar and Monticello on US 278. The new expressway would parallel US 425. 
The Arkansas State Highway and Transportation Department (ATHD) has begun right-of-way acquisition as of late 2002, and plans to let contracts starting in 2003.  Out of the estimated $300 project cost, the state has secured about $100 million, including a diversion of funds once assigned to widening US 425.
The I-530 extension was added to I-69 plans to placate former congressman Jay Dickey (R - Ark.), who originally wanted I-69 to split into two routes between El Dorado and Memphis. One route would cross the Mississippi River near Memphis, and the other near Greenville, Miss. This plan was given the painful-sounding nickname "Dickey Split." 
Nonetheless, there was still dissent at the end of 2002 over where funds would be spent and where construction would start first. Advocates to the south feared that the state would start at Pine Bluff, where there was more traffic, then lose interest in completing the southern portions. An early January 2003 compromise was drafted: two-lane and four-lane sections will be started at both ends of the I-530 extension, and some of the diverted US 425 funds would be given to US 65 and US 167 improvements. 
Our New Highway Extension Technique is Unstoppable
A Lousiana candidate for Congress in fall 2004 proposed extending I-530 a little bit further: to I-49 in Alexandria, La. via Monroe. In September 2004, Jock Scott, running for the 5th District, said:
I hereby propose the construction of Interstate 530 from Monroe to Alexandria, and to the Arkansas line. The 5th District, the Northeast Quarter of Louisiana, is the most neglected section of Louisiana, our worst highway system. We must begin now to make Interstate 530 a Louisiana reality. 35 years ago, led by Bennett Johnston, Louisiana began advocating a North-South Highway System for Louisiana, Y-shaped with legs from Alexandria to both Shreveport and Monroe. But only one-half of it was built, I-49 from Lafayette to Shreveport. We must complete this project. Now our new Interstate 530 will connect Lafayette, Alexandria, Monroe and Arkansas. No plans were in place at the time to extend I-530. Scott's proposal, which would probably follow the US 425 and US 165 corridors, would add about 250 miles to I-530, making it nearly 300 miles long, far longer than today's longest 3di, the 129-mile I-476.
Scott's reasons for extending the highway: economic growth, trade, and jobs. "With a North-South Interstate 530 complimenting Interstate 20, the Monroe-Ruston region will become a commercial powerhouse, a major transportation crossroads, a major distribution center," Scott told BayouBuzz.com. (He probably meant to say "complementing".)
7.40 miles ; Interstate 630 runs through Little Rock, connecting I-30 and I-430.
It was apparently conceived in the 1960s as the "8th Street Expressway",  and was started in the early 1970s. The final eastern mile or so encroached on two parks, and was the subject of litigation in the mid-1970s.  It was completed in the late 1980s.
I-630 won a U.S. "Design for Transportation" award in 1982 for the bikeway in its right-of-way. I don't know if this was done as mitigation in the disputed section.
I-730 (proposed) Arkansas
So far, this is just a proposal from the Greater Jonesboro [Ark.] Chamber of Commerce, but Arkansas interstate proposals have had a very good track record recently.
US 67, from Little Rock to Newport and beyond, is proposed as an extension of Interstate 30 (though some propose a southward extension of I-57 along the same route). State route 226, a connector from US 67 to Jonesboro, is slated for a widening to four lanes. What the Jonesboro C of C wants is a new freeway near AR 226 to connect future I-30 and US 63 (future I-555 in Jonesboro. This would provide a desired interstate link to the state capital.
"We just named it I-730," said Chamber executive vice president Cari White, "because it seemed like the thing to do because it would come from I-30 at Newport through Gibson Switch and up through I-555."