As mentioned, the ghosts in PacMan generally don't actually use a particularly intelligent algorithm but rather rely on the combination of a number of simple rules to give the appearance of intelligent chasing; if you do it well they can even seem like they're working together.

Typical rules you might apply to any given ghost include:

• Stick close to the centre, attack the player if (s)he comes close.
  
• Patrol the outer edge of the board, attack the player if (s)he comes close.
  
• Attempt to vertically align with the player, then move closer horizontally.
  
• Attempt to horizontally align with the player, then move closer vertically.
  
• Move randomly (a single random ghost often keeps things mixed up nicely).

Basically have the ghosts each follow one or two rules, but switch to heading straight for the player once they get within a certain distance.

Also already mentioned, a lot of implementations only allow the ghosts to change direction if they're at an intersection, which can help to give the player a chance.

Many implementations also give each ghost a "home quadrant" - you might notice in versions that include this that the ghosts will each initially head to a specific corner of the board before starting to follow thier other rules, and may even return to thier "home corner" if the player gets far enough away from them - this generally ensures that there will be a ghost in each corner of the grid unless the player intentionally leads them away.


A* or Dijkstra would both work perfectly fine if you want to practice using them though, so if you're interested then give it a try! You can always change things later if your chosen solution doesn't turn out fun to play or is too smart or stupid. Pretty much any pathfinding will work out for you, but you'll find that you don't need anything particularly complex for a good PacMan AI.

One other thing you may want to keep in mind is that you might not always want to calculate the shortest path to the player; you can often get good results by attempting to guess where the player is going and trying to cut them off, especially if another ghost is chasing them.

Dijkstra's algorithm is probably your best bet if you want the game to be absolutely impossible. The graph is fairly small, so A* shouldn't be necessary. However, if you're looking for a more realistic clone, the AI is well documented.

The original Pacman had very specific AI. The each of four ghosts each had their own job:

Orange: 'Pokey' - Wanders around at random; is the slowest.
Pink: 'Speedy' - Also wanders at random, but is the fastest.
Cyan: 'Bashful' - Avoids Pacman at first, but retaliates if attacked.
Red: 'Shadow' - Chases the player at all times.

Also, when given two equal choices of where to go, Speedy and Pokey (also Bashful and Shadow) will turn in opposite directions to one-another, increasing the chance of boxing Pacman in.

Regards
Admiral

Edit: Take a look here for a discussion.

What I did for my chaser was:
Only change direction at an intersection.
To decide which way to go, loop through each of the possible squares it can go to (1st square in each direction), then calculate the straight-line distance from that square to pac-man. Then go in the direction that produces the shortest distance.

Very simple and effective method.

Degra

I believe the system used in the original arcade version was based on the game storing what the player last did at each junction in the maze and then the ghosts would check that and use it or not on a random value that was set according to the current level of the game.