Yes! Errr... NO!
There are three competing theories on this.
Jesus went to Hell with the damned.
Jesus went to paradise in Hades
Jesus went to heaven.
All of these beliefs are based on a few critical verses.
Verse 1: 1 Peter 3:18-20
In 1 Peter 3:18-20 (NIV), we see:
18 For Christ also suffered once for sins, the righteous for the unrighteous, to bring you to God. He was put to death in the body but made alive in the Spirit.
19 After being made alive, he went and made proclamation to the
imprisoned spirits— 20 to those who were disobedient long ago when God
waited patiently in the days of Noah while the ark was being built. In
it only a few people, eight in all, were saved through water,
This supports (pretty conclusively) beliefs 1 and 2 by stating that Jesus, in the spirit, went to speak to the "imprisoned souls".
Verse 2 Luke 23:43
We see in Luke 23:43 (KJV)
43 And Jesus said unto him, Verily I say unto thee, Today shalt thou
be with me in paradise.
This pretty conclusively states that he went to paradise. This supports beliefs number 2 and 3.
Verse 3 Luke 23:46
Luke 23:46 (NIV) states:
46 Jesus called out with a loud voice, “Father, into your hands I
commit my spirit.” When he had said this, he breathed his last.
The idea is that Jesus definitely didn't go to hell, since he committed his spirit into the Father's hands. Therefore, this is used to support beliefs 2 and 3.
Vers 4 Ephesians 4:9
This verse is often used to say that Jesus "descended into hell" or "the depths" or something (NIV)
9 (What does “he ascended” mean except that he also descended to the
lower, earthly regions?
However this doesn't really hold water since the reference point of the ascension means that he really descended to earth. Also, the translation "lower, earthly regions" supports the idea that he descended to Earth rather than other translations which state "lower earthly regions" (notice the lack of the comma, which is an invalid translation).
This verse is often used to support belief #1.
So, which belief is correct? This is something that is difficult to see.
1 Cor. 13:12 (KJV)
12 For now we see through a glass, darkly; but then face to face: now I
know in part; but then shall I know even as also I am known.
I should note another idea that supports belief #2 is the fact that there are two different words for "Hell". One is the fiery pit referred to in Revelations and one is the place called "Hades". Unfortunately, we don't have any good, solid definition for "Hades", so some have interpreted that as the "paradise" that Jesus was referring to on the cross. This interpretation is used to support that second belief.
Read this article for much more information.