Onedayers
Pakistan has the honours.
http://www-aus.cricket.org/link_to_database/STATS/ODIS/BATTING/ODI_BAT_MOST_RUNS_OVER.html
Runs Batsmen Bowler
30 ST Jayasuriya (x4066661) Aamer Sohail SL v Pak Singapore 1995-96
30 ST Jayasuriya (666642) CZ Harris SL v NZ Sharjah 2000-01
28 Shahid Afridi (662644) ST Jayasuriya Pak v SL Nairobi 1996-97
28 SR Tendulkar (4B26444)
A Jadeja (L) CJ Drum Ind v NZ Hyderabad 1999-2000
28 Shahid Afridi (666064) Enamul Haque Pak v Ban Dhaka 2001-02
27 Asif Mujtaba (41)
Saleem Malik (6466) M Muralitharan Pak v SL Colombo 1994-95
27 Rameez Raja (41)
Moin Khan (4666) IR Bishop Pak v WI Sharjah 1995-96
27 MS Atapattu (1)
ST Jayasuriya (66446) Akram Khan SL v Bdesh Colombo 1997-98
27 Z Khan (1666x6)
AB Agarkar (1) HK Olonga Ind v Zim Jodhpur 2000-01
27 Imran Nazir (1)
Shahid Afridi (64646) GE Bradburn Pak v NZ Sharjah 2000-01
27 SM Pollock (266661) JEC Franklin RSA v NZ Perth 2001-02
27 DS Lehmann (1)
B Lee (64646) AA Donald Aus v RSA Perth 2001-02
26 RW Marsh (64646W) BL Cairns Aus v NZ Adelaide 1980-81
26 BL Cairns (464660) VBJ John NZ v SL Colombo 1983-84
26 MW Gatting (6066B6) RJ Shastri Eng v Ind Jullundur 1981-82
26 RJ Hadlee (xx64241)
MD Crowe (4) GA Gooch NZ v Eng Manchester 1986
26 IT Botham (442466) SP Davis Eng v Aus Perth 1986-87
26 AP Kuiper (2042666) CJ McDermott RSA v Aus Centurion 1993-94
26 Saeed Anwar (226664) A Kumble Pak v Ind Madras 1996-97
TEST
Here also pakistan has the distinction.
http://www-aus.cricket.org/link_to_database/STATS/TESTS/BATTING/TEST_BAT_MOST_RUNS_OVER.html
Runs Batsmen Bowler
26 CD McMillan (444464) Younis Khan NZ v Pak Hamilton 2000-01
25 AME Roberts (46266L) IT Botham Eng v WI Port-o-Spain 1980-81
25 B Sutcliffe (66061) HJ Tayfield NZ v RSA Johannesburg 1953-54
RW Blair (600)
25 NJ Astle (666L 0) AR Caddick NZ v Eng Christchurch 2001-02
CL Cairns (41)
24 JFM Morrison (2x6 3x4) Imran Khan NZ v Pak Karachi 1976-77
24 SM Patil (4440444) RGD Willis Ind v Eng Manchester 1982
24 IT Botham (464604) DA Stirling Eng v NZ The Oval 1986
24 Kapil Dev (006666) EE Hemmings Ind v Eng Lord's 1990
24 IDS Smith (244266) AS Wassan NZ v Ind Auckland 1989-90