Wikipedia is full of lists. One I came across recently is a list of players who hit a home run in their first at bat. I've checked some other sources as well and it looks like the Wikipedia list is up-to-date. On average, this is a pretty rare feat. Only 114 batters have done this since the first guy did it in 1885. That works out to less than 1 per year. But it's becoming more common. In the past 10 years (2003-2012) it's been done 32 times! Working backwards here's Part 1 of the list since 2003.
Apparently hitting a home run in your first at bat is not an indication of future performance.
2012 Topps Pro Debut #81 Jurickson Profar
8/2/12. Eddy Rodriguez. I don't have a card for this guy. He appeared in 2 games for the Padres and was 1 for 7. Currently playing for the Padres AA team in San Antonio.
2013 Topps Opening Day #167 Starling Marte
7/26/12: Marte hit 5 home runs in 47 games for the Pirates last year and looks to be the starting left fielder this year. He's hit one home run already in 2013.
2012 Topps Update #209 Yasmani Grandal
2012 Topps Allen & Ginter #192 Brett Pill
2012 Topps Golden Moments Parallel #40 Tom Milone
2011 Bowman Platinum Prospects X-Fractors #80 Brandon Guyer
2012 Bowman Chrome #124 J. P. Arencibia
2010 Bowman Platinum #42 Daniel Nava
2010 Topps 206 #24 Starlin Castro
5/7/10: Castro, while not necessarily a home run hitter, is by now, a 2-time All-Star with a near .300 batting average.
2008 Bowman Chrome Draft Prospects #95 Luke Hughes
2007 Bowman Draft Draft Picks Gold #54 Jason Heyward
2010 Upper Deck #31 John Hester
8/28/09: Hester has not had much playing time since his big moment and is currently with the Angels AAA team in Salt Lake City.
2009 Topps Update #154 Gerardo Parra
2009 Topps Heritage #610 Jordan Schaffer
2009 Upper Deck #406 Mark Saccomanno
2009 Topps 206 #105 Lou Montanez