I remember when I first started playing I told my teacher "I want to play something that sounds cool!" So I figured that you're thinking the same thing. :^)

Here is the tab for a very common blues progression in A that not only sounds cool, but will stretch and exercise your fingers at the same time.

A
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--7--7--9--7--|--7--7--9--7--|--7--7--9--7--|--7--7--9--7--|
--5--5--5--5--|--5--5--5--5--|--5--5--5--5--|--5--5--5--5--|

D
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--7--7--9--7--|--7--7--9--7--|--7--7--9--7--|--7--7--9--7--|
--5--5--5--5--|--5--5--5--5--|--5--5--5--5--|--5--5--5--5--|
--------------|--------------|--------------|--------------|


A
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--7--7--9--7--|--7--7--9--7--|--7--7--9--7--|--7--7--9--7--|
--5--5--5--5--|--5--5--5--5--|--5--5--5--5--|--5--5--5--5--|

E                               D
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--9--9--11-9--|--9--9--11-9--|--7--7--9--7--|--7--7--9--7--|
--7--7--7--7--|--7--7--7--7--|--5--5--5--5--|--5--5--5--5--|
--------------|--------------|--------------|--------------|


A                               E
--------------|--------------|--------------|--------------|
--------------|--------------|--------------|--------------|
--------------|--------------|--9--9--9--9--|--9--9--9--9--|
--------------|--------------|--9--9--9--9--|--9--9--9--9--|
--7--7--9--7--|--7--7--9--7--|--7--7--7--7--|--7--7--7--7--|
--5--5--5--5--|--5--5--5--5--|--------------|--------------|

* Play the last two measures of the E chord with your 1st finger on the 7th fret and your 3rd finger barring the two notes on the 9th fret.
(Repeat)

Play it for a couple of days and make sure you are not getting any fret buzz by pushing hard enough on the strings. Your pinky will probably be the most difficult.

Once you have a feel for it, get your tape recorder and record it. Repeat it about 4 times if you can, without wearing out your grip. Don't worry if it's not perfect! This is practice.

Now once you've got it on tape, and rested a little while, play the following A Pentatonic scale forward and backward against what you have just recorded. Voila! Instant jam session!
 

  A   C   D   E   G   A   C   D   E   G   A   C
------------------------------------------5---8---
----------------------------------5---8-----------
--------------------------5---7-------------------
------------------5---7---------------------------
----------5---7-----------------------------------
--5---8-------------------------------------------


Memorizing both the progression and the scale is imperative if you want to learn to improvise. To improvise this scale, just start mixing up the order in which you play the notes. Skip strings too. Try playing one note per string. This is how songs are born!

Practice both of these diligently and the next thing you know, your fingers will be able to handle even more challenging tasks.