How often does a block have only one transaction? I was looking at blocks on blockchain.info, and came across this one with only one transaction in it: (the mining reward one)

https://blockchain.info/block-index/512049/00000000000000000429a0c4fbe735b2d8b493daedf0207728543f748c262437

Is that at all suspicious? Does it mean someone was trying to block some transactions from going through? How common are single-transaction blocks?
It's possible that this could happen just because there aren't any transactions to be mined. Early on in the bitcoin block chain, this was often the case. This could also happen if two blocks are solved on top of each other in a very short amount of time, with not much time for new transactions to be broadcasted in between. Today, however, more often than not this is due to a miner trying to get his/her block out to the rest of the peers on the network as soon as possible. 

A miner would want to do this because bigger blocks take longer to propagate to the rest of the network. Nodes have to download and verify the validity of a block before they can relay them to their peers, because if they don't verify before sending and they send an invalid block, then their peers may ban them and the node will have no one to connect with on the network.

Think of it this way. If your block takes 50 seconds to get out to 90% of the peers on the network, and someone else mines a block 1 second later than you but can get their block out to 90% of the network in 9 seconds, who do you think will have the greater chance of getting their block accepted by more peers?

It may also be worthwhile to note that while this seems like it has a better pay off, it also sends a message to everyone on the network that the miner who mined the block doesn't really actually care about the bitcoin network's transactions, it just cares about its reward. And if the miners don't support the system, then why should investors or anyone else have confidence in it? I guess what I'm trying to say is that if a lot of miners did this, then the price of bitcoin would likely drop as it would show a lack of faith in the system.

There's a more mathematical analysis of orphan rates and payoffs here: http://organofcorti.blogspot.com/2013/10/161-network-orphaned-blocks-part-1.html\

In addition, it may interest you to know that there is a new proposal to enable faster propagation of blocks even if they are very large. See here for more info: https://gist.github.com/gavinandresen/e20c3b5a1d4b97f79ac2. 



A different way of explaining this would be that, for a block to be accepted by the network, it has to be propagated out and checked by everyone. While blocks are spreading through the network, any miners who don't know about the new block will just keep mining on the block they have. In most cases, probably, this is just wasted work since there is already a block that is on it's way to being accepted. But if your block is much smaller (i.e. very few txs), then it gives other miners less time to solve a block while yours is propagating, and it also increases your chance that your block will get accepted by the majority of the miners even if someone else solved a block slightly before you.



To answer this question with a bit of data, I made a script that processed the last 1 month of blocks (4,464 blocks before and including block 338,782), and gathered data about the number of transactions in each block. These were the results.


  From this data, it seems that roughly
  
  
  1.3% of blocks are solved with just the reward transaction
  1.6% of blocks are solved with fewer than 10 transactions. 
  


# Transactions  # Blocks with transaction count in MIN-MAX range
MIN     MAX     COUNT 
0       9       73
10      19      31
20      29      22
30      39      74
40      49      52
50      59      43
60      69      107
70      79      50
80      89      41
90      99      56
100     109     55
110     119     50
120     129     86
130     139     46
140     149     54
150     159     57
160     169     51
170     179     62
180     189     49
190     199     53
200     209     46
210     219     45
220     229     64
230     239     42
240     249     45
250     259     69
260     269     58
270     279     39
280     289     41
290     299     41
300     309     44
310     319     45
320     329     37
330     339     35
340     349     45
350     359     42
360     369     40
370     379     42
380     389     41
390     399     37
400     409     48
410     419     47
420     429     42
430     439     40
440     449     40
450     459     46
460     469     42
470     479     32
480     489     33
490     499     40
500     509     38
510     519     68
520     529     44
530     539     28
540     549     32
550     559     28
560     569     35
570     579     27
580     589     29
590     599     28
600     609     19
610     619     31
620     629     20
630     639     27
640     649     38
650     659     28
660     669     27
670     679     25
680     689     18
690     699     21
700     709     27
710     719     28
720     729     23
730     739     25
740     749     25
750     759     19
760     769     21
770     779     24
780     789     27
790     799     23
800     809     16
810     819     18
820     829     19
830     839     18
840     849     16
850     859     19
860     869     20
870     879     16
880     889     18
890     899     16
900     909     24
910     919     24
920     929     14
930     939     18
940     949     20
950     959     12
960     969     13
970     979     15
980     989     15
990     999     21
1000    1009    15
1010    1019    15
1020    1029    18
1030    1039    14
1040    1049    13
1050    1059    13
1060    1069    9
1070    1079    16
1080    1089    16
1090    1099    8
1100    1109    17
1110    1119    10
1120    1129    12
1130    1139    8
1140    1149    8
1150    1159    22
1160    1169    10
1170    1179    14
1180    1189    17
1190    1199    10
1200    1209    11
1210    1219    14
1220    1229    9
1230    1239    9
1240    1249    12
1250    1259    9
1260    1269    8
1270    1279    7
1280    1289    7
1290    1299    9
1300    1309    8
1310    1319    12
1320    1329    8
1330    1339    7
1340    1349    12
1350    1359    10
1360    1369    13
1370    1379    10
1380    1389    10
1390    1399    9
1400    1409    10
1410    1419    8
1420    1429    14
1430    1439    10
1440    1449    6
1450    1459    6
1460    1469    6
1470    1479    9
1480    1489    7
1490    1499    4
1500    1509    5
1510    1519    8
1520    1529    5
1530    1539    12
1540    1549    3
1550    1559    7
1560    1569    8
1570    1579    3
1580    1589    7
1590    1599    2
1600    1609    12
1610    1619    5
1620    1629    10
1630    1639    3
1640    1649    4
1650    1659    5
1660    1669    6
1670    1679    5
1680    1689    3
1690    1699    5
1700    1709    2
1710    1719    1
1720    1729    10
1730    1739    4
1740    1749    5
1750    1759    4
1760    1769    4
1770    1779    2
1780    1789    3
1790    1799    6
1800    1809    3
1810    1819    2
1820    1829    4
1830    1839    5
1840    1849    4
1850    1859    3
1860    1869    3
1870    1879    3
1880    1889    5
1890    1899    3
1900    1909    3
1910    1919    4
1920    1929    1
1930    1939    0
1940    1949    3
1950    1959    0
1960    1969    0
1970    1979    3
1980    1989    2
1990    1999    2
2000    2009    3
2010    2019    3
2020    2029    3
2030    2039    3
2040    2049    7
2050    2059    3
2060    2069    1
2070    2079    4
2080    2089    2
2090    2099    1
2100    2109    1
2110    2119    3
2120    2129    2
2130    2139    2
2140    2149    4
2150    2159    1
2160    2169    2
2170    2179    1
2180    2189    2
2190    2199    3
2200    2209    0
2210    2219    0
2220    2229    1
2230    2239    0
2240    2249    3
2250    2259    0
2260    2269    1
2270    2279    2
2280    2289    1
2290    2299    3
2300    2309    0
2310    2319    1
2320    2329    0
2330    2339    1
2340    2349    1
2350    2359    1
2360    2369    1
2370    2379    1
2380    2389    0
2390    2399    0
2400    2409    1
2410    2419    1
2420    2429    1
2430    2439    0
2440    2449    0
2450    2459    0
2460    2469    1
2470    2479    0
2480    2489    0
2490    2499    2
2500    2509    0
2510    2519    0
2520    2529    1
2530    2539    2
2540    2549    2
2550    2559    1
2560    2569    0
2570    2579    1
2580    2589    1
2590    2599    0
2600    2609    0
2610    2619    0
2620    2629    0
2630    2639    0
2640    2649    2
2650    2659    0
2660    2669    0
2670    2679    0
2680    2689    0
2690    2699    0
2700    2709    0
2710    2719    0
2720    2729    0
2730    2739    0
2740    2749    0
2750    2759    0
2760    2769    0
2770    2779    0
2780    2789    0
2790    2799    0
2800    2809    0
2810    2819    1
2820    2829    0
2830    2839    0
2840    2849    0
2850    2859    1
2860    2869    0
2870    2879    0
2880    2889    0
2890    2899    0
2900    2909    0
2910    2919    0
2920    2929    0
2930    2939    0
2940    2949    0
2950    2959    0
2960    2969    0
2970    2979    0
2980    2989    0
2990    2999    0
3000    3009    0
3010    3019    0
3020    3029    0
3030    3039    1
3040    3049    0
3050    3059    0
3060    3069    0
3070    3079    0
3080    3089    0
3090    3099    0
3100    3109    0
3110    3119    0
3120    3129    0
3130    3139    1




The x-axis here (it may be hard to read) is the transaction range (each MIN-MAX pair in data above represents one column). The y-axis shows the number of blocks in the last month that had a transaction count within the range.