"Celtic Cross; A celtic kruis is a combination of a Christian kruis with a circle. It's the symbol of the Keltic Christianity, Irish Christianity. Under the kruis Alex has tattooed his datum of brith, April 10th 1990. Alex' feelings about the Celtic kruis aren't known.
What goes around comes around; In an interview Alex has zei that he isn't a Buddhist, but he does believe in some of their beliefs. He believes in "What comes around goes around".
ER; Many people are thinking that the two linked hearts with E R in it refers to Emma Roberts. But he says that that isn't true. No, he claims to be a big fan of the British queen, Elizabeth the second. The E and the R should refer to Elizabeth Royal. When he "left" to California he wanted something to remind him about her.
Emma; Alex has a tattoo which says "Emma" at his ringfinger. He did this at the end of 2008. In an interview Alex admitted having the name of a girlfriend tattooed on his ringfinger. Not long after that, they broke up. It's about Emma Roberts. At the moment he covers it up.
Arabic script; On the inside of his forearm he has an Arabic script tattooed. It says "Your mind is stronger than your body".
アレックス; Below his waist he's got his name tattooed in Japanese." link He also has another tattoo, but I can't find the artikel where he mentioned where it was. There isn't a lot of information on it though.
ETA - Alex got another tattoo "Little Lamb" on his left wrist which may refer to his current girlfriend, Dianna Agron. I'm guessing since her Twitter account is alittlelamb and she has a tattoo "Mary had a Little Lamb".