To make cutting easier, score the bars with a knife as soon as they come out of the oven, using a ruler as a guide.  Let the bars or brownies cool completely in the pan on a wire cake rack and freeze* until they firm, making the job of cutting along the scored lines easier . *Do not freeze bars with perishable fillings. Let chill in the refrigerator for the appropriate time; the filling must be firm and not runny before cutting. 

Some tips: 

Always grease the baking pan with shortening, butter or nonstick cooking spray, whether the recipe calls for it or not. In my experience, shortening or Baker's Joy shortening, works the best.

In general, for easy removal, grease the pan, line it with parchment paper and then grease the side showing, as well. To remove, run a paring knife around the inside edge of the pan and then invert the pan onto a flat surface and peel off the parchment. 

Bar cookies can be lifted from their pan with an aluminum foil "sling" prepared in advance, making it easier to cut them. However, an exception are those made with a delicate shortbread base (like lemon bars) or those with loose or runny fillings; they should be cut in their pans. When the bar cookies have cooled, simply pull up foil with its contents, place on a flat surface and remove. You can cut them with an electric knife (my favorite way because you don't crush the bars) or a sharp knife. For bars to boast of and pretty enough to package up and give away, first trim away the outer dry edges of the bars, as well. 

To cut squares with soft or gooey bars like Brownies in their pan, move the knife across the pan in an up and down sawing motion from one end to the other until they are cut. I often throw mine in the freezer until somewhat hardened if my brownies are particularly gooey; it helps make the cutting job easier. A hot knife will make the bars cut more easily: before starting, dip the sharp knife in hot water and wipe with a dry kitchen towel. When cutting gooey brownies or a similar type of bar, try not to press down with the knife or the cut edges will squish together. They will also easily crack on top, too. After each cut, clean and warm the knife by dipping it in hot water and wiping with a dry kitchen towel before resuming. 

To cut squares with runny fillings or toppings, such as Lemon Bars, use a large sharp chef's knife, a bench scraper or the edge of a metal spatula AFTER the bars have been chilled for the appropriate time. I prefer to use a bench scraper because it cuts in neat, even squares. To use, simply press down to cut through the baked bar.