Resident visa holders in Gulf Cooperation Council countries (GCC) (Bahrain, Kuwait, Oman, Qatar, Saudi Arabia) of any nationality might be able to obtain a visit visa on arrival in the UAE. Confirm with an airline, UAE embassy, or UAE immigration department before travelling though, information about this type of visa seems to be sketchy (possibly to allow passport control officers more flexibility in admitting or rejecting travellers when they arrive in the UAE).

Visitors should be of a higher-level profession (doctor, engineer, professor, teacher, lawyer, manager, etc).
Valid passport with valid GCC residence stamp is required, along with proof of employment in the country of residence (residence stamp in passport might be sufficient, or bring labour card and/or letter from employer stating job title).
Visa fee is apparently AED 100 but some reports of visitors paying up to AED 200 as an entry fee.
Probably renewable once for AED 500-600 (some sources say not renewable but that might be old information).

Dubai DNRD website says "GCC nationals (Resident) - To be issued to GCC resident nationals and those who accompany them. Fees: AED 165 e-form fees. Valid for 30 days and renewable once for a similar period (30 days). Renewal fees AED 620 (e-form fees)." which sort of sounds like they're referring to GCC citizens rather than any GCC resident. But GCC citizens have visa-free entry to the UAE anyway. And it's not clear if pre-travel application is required or if it is available on arrival in the UAE.

UAEinteract.com (a UAE government supported website) says "The following categories of visitors may receive their visit visa at the airport, upon arrival. 1. AGCC Residents who are not GCC nationals but who have a high professional status such as company managers, business people, auditors, accountants, doctors, engineers, pharmacists, or employees working in the public sector, their families, drivers and personal staff sponsored by them, are eligible for a non-renewable 30-day visa upon arrival at the approved ports of entry." That might be out-of-date information after the change in visa rules in July 2008.

The Sharjah Airport website says "GCC country residence visa holders: Certain category of visa holders of GCC Countries can enter the UAE and the visa will be issued up on their arrival. Prior approval is not required." Exactly what categories are being referred to is not clarified.