Power Transistors

I'm not too familiar with the transistor market so I was hoping someone could propose a transistor that would fit my needs. Currently I am using a BJT NPN general purpose transistor in a project I am working on. With a Base Emitter voltage of .7V and a Collector Emitter voltage of 5V, I am getting an Emitter current of about .25A.

I would like a current of .75 - 1 A with the same Collector Emitter voltage of 5V. Any suggestions would be appreciated.

The base of a transistor is driven with current, not voltage. They all have a base-emitter voltage of about 0.6V to 0.8V depending on how much current but their current gain is different. You need to say how much base current your circuit can supply when the transistor conducts 1A.
Since you want 5V across the transistor and a current of 1A then the transistor must be a power type with a heatsink to dissipate 5W.

A TIP31 transistor needs a base current of at most 40mA when the collector to emitter current is 1A.

A TIP120 darlington transistor needs a base current of at most only 1mA, but its base voltage is about 1.4V.

Thanks for the help, I had forgotten that BJTs are current driven. I've gone ahead and ordered the TIP31s, they seem appropriate for my purposes.