Do I need a pick to play guitar?

Not only does it depend on preference of sound, but also style.  I personally have only ever used finger picking because I was taught the classical guitar, but I know using a pick is much more common for acoustic and electric players.  I keep my left hand's nails grown out long, and if you can get them long enough then they sound just fine on the strings.  A pick always makes the notes a little crisper, but I prefer nails because it matches the mellow tone of my nylon strings.  And of course, it's perfectly fine to practice both techniques!  Variety and experience in more areas is all the better!  

You only need a pick for strumming.  I used to switch back and forth between strumming and finger picking i kept a pick behind my right ear tucked into my hair when i used to play at an open mic or competition or something like that.  Using a pick when you are using chords is ideal and when doing runs too, it produces a crisper sound when i play

There are plenty of players who use fingers rather than a pick, Mark Knopfler and Jeff Beck for example.

I doubt you'll get exactly the same sound with your fingers as you will with a pick but it's up to you to use whichever you want. There are lots of things you can do with fingers that can't be done with a pick.

Use whatever gets the sound you want. I’ve seen players use either or various combinations.

Using a pick creates a different sound from playing with fingers.  It is also easier on your fingernails.  And what do you do if your nail breaks?  

I actually like the sound without the pick.  I would say it is good to be able to play both ways.