Centering diagrams made with tikz-cd

The reason for this is that the curved arrows define helper coordinates that are placed far outside the drawn parts of the diagram, so the diagram contains a lot of whitespace, and its width is actually wider than the width of the text block. Look in the log and you'll see a warning about an Overfull \hbox (72.53682pt too wide). To visualize this, add the backgrounds TikZ library, and add [show background rectangle] to the options of the tikzcd environment. (See code below.)

To fix it, add overlay to the options of the \ar commands that draws the arrow. This option means that those commands will not be taken into account when the bounding box of the diagram is defined.

\documentclass{article}
\usepackage{tikz-cd}
\usetikzlibrary{matrix,arrows,backgrounds}
\begin{document}
The diagram is not perfectly centered:
\[
\begin{tikzcd}[show background rectangle]
H^0(U\cup V) \rar & H^0(U)\oplus H^0(V) \rar & H^0(U\cap V) 
\ar[out=-20, in=160]{dll} \\
H^1(U\cup V) \rar & H^1(U)\oplus H^1(V)\rar & H^1(U\cap V) 
\ar[out=-20, in=160]{dll} \\
H^2(U\cup V) \rar & H^2(U)\oplus H^2(V)\rar & H^2(U\cap V) 
\end{tikzcd} 
\]
The diagram is centered:
\[
\begin{tikzcd}[show background rectangle]
H^0(U\cup V) \rar & H^0(U)\oplus H^0(V) \rar & H^0(U\cap V) 
\ar[overlay,out=-20, in=160]{dll} \\
H^1(U\cup V) \rar & H^1(U)\oplus H^1(V)\rar & H^1(U\cap V) 
\ar[overlay,out=-20, in=160]{dll} \\
H^2(U\cup V) \rar & H^2(U)\oplus H^2(V)\rar & H^2(U\cap V) 
\end{tikzcd} 
\]
\end{document}

No such problem for a commutative diagram made with pstricks. Loading auto-pst-pdf enables you to compile with pdflatex, provided it is launched with the -shell-escapeswitch (TeX Live, MacTeX) or --enable-write18.

\documentclass{article}

\usepackage[showframe]{geometry}%
\usepackage{pst-node, auto-pst-pdf}%

\begin{document}

\[\begin{psmatrix}[rowsep =5ex]
    H^0(U \cup V) & H^0(U) \oplus H^0(V) & H^0(U \cap V)\pnode[0,0.15]{S1}\\
    \pnode[0,0.08]{S2}H^1(U \cup V) & H^1(U) \oplus H^1(V) & H^1(U \cap V)\pnode[0,0.15]{S3} \\
    \pnode[0,0.08]{S4}H^2(U \cup V) & H^2(U) \oplus H^2(V) & H^2(U \cap V)
    \psset{arrows=->, linewidth=0.5pt, nodesep=4pt, arrowinset=0.12}
    \ncline{1,1}{1,2}\ncline{1,2}{1,3}
    \ncline{2,1}{2,2}\ncline{2,2}{2,3}
    \ncline{3,1}{3,2}\ncline{3,2}{3,3}
    \psset{angleA=-15,angleB=165, ncurv=0.8, nodesepB=2pt}
    \nccurve[angleA=-15,angleB=165, ncurv=0.8, nodesepB=2pt]{S1}{S2}%{1,3}{2,1}
    \nccurve{S3}{S4}
  \end{psmatrix}\]

\end{document}