Why Did Isildur Cross the River?

[Boromir88]

I wouldn't say it was Isildur's pride which led him to pick his route, and I would not overestimate the sway the Ring may have played.

"I cannot use it. I dread the pain of touching it. And I have not yet found the strength to bend it to my will. It needs one greater than I now know myself to be. My pride has fallen. It should go to the Keepers of the Three."~Unfinished Tales: Disaster of the Gladden Fields

Isildur's failure to master the Ring, appears to have caused a significant blow to his pride. To the point where he is no longer boasting about being the one who dealt the "death blow," and claiming the Ring as an heirloom, but seriously contemplating handing it over to Elrond. Whether Isildur would have followed through or not is another question, but if the Ring could pick up that Isildur was taking it to Rivendell (a dangerous place for the Ring to end up!) then it could have played a factor. Afterall, it did seem to draw the orcs attention.