How can I escape from deep lakes?

If you're lucky enough to end up in a lake with rock or dirt sides (not sand) you can dig 3 sideways into the bank and 2-3 up to create an air pocket to jump up into:

######~~~
###++#~~~
###++#~~~
###~~#~~~
###~~~~~~
###~~~~~~
###~~~~~~
#########

# = Dirt / rock / other block
~ = Water
+ = Precious life giving air

From there you can dig your way out. I've done this so often I can now do it in pitch black darkness. Maybe I should learn to look before I leap...

Get yourself some flippers so you can swim out, or a grappling hook to climb. I believe rocket boots would also work underwater, though they're rare.

A breathing reed would give you a little better chance of not drowning, and a balloon would improve your jump height.

If none of these options are available, you can try digging an air pocket, as explained in this answer.

Build a solid area around yourself with mud or dirt, make the ceiling 2-3 blocks high, then mine out an air pocket.

This is sort of like Stuart Pegg's answer above, but doesn't require a solid wall next to you.

 NNNN
 NXXN
 N  N
 N  N
DDDDDDD
DDTDDDD 

D - dirt
N - new dirt you add
X - spots where you add dirt, then mine it away
T - mine this spot out and put a torch there, so you can see